To the ancient Greeks, the arrival of Asklepios was unreservedly welcome; his cult took hold immediately and grew quickly upon its introduction. This was a god both wanted and needed--kind-hearted, helpful, and with a great interest in the welfare of humanity.
To modern pagans, however, Asklepios is almost a forgotten god. Even among Hellenic pagans, his aid is not commonly sought and he receives few honors. I've never quite understood this, since in my experience he is very much an active, present deity who is more than willing to work with us to find cures for our ailments.
A son of Apollo by the nymph Koronis, Asklepios' birth was spectacularly mythological: when Apollo learned that Koronis had been unfaithful to him, he sent Artemis to destroy her, saving their child at the last possible minute by taking him from her on her funeral pyre. He learned the healing arts from the centaur Cheiron and became a healer of great skill. Eventually he attempted not only to heal the sick but to raise the dead, an act that prompted great objections from Hades and Asklepios' resulting death at the hands of Zeus. (Gantz 91)
The Greeks had a long-standing tradition of honoring heroes in cult. Typically a hero was a local entity with an interest in the city or region in which he had a mythological history or in which his body rested; the cult was centered around the hero's grave or heroon, where the hero received sacrifices and votive offerings. He might also be provided with an upgraded grave marker (Burkert 203), or with a festival or festivals. While hero-cult did not exist in all parts of Greece (Garland 32), it was not uncommon. Unlike the gods, whose influence might be split--and the Iliad shows the problems this could cause--a hero could be counted on to protect the interests of the community (Garland 97). A city's founder, whose interest in the well-being of the city would be natural and undoubted, often became a hero. However, a hero need not be originally a member of the community, as is shown by Athens' efforts to find the bones of Theseus on the island of Skyros and move them to Athens, where the Athenians would pay cult to the new addition and receive the subsequent benefits (Garland 82-98).
A hero was considered to be a chthonic being and received the honor--blood offerings, food, libations--appropriate to such a being (Burkert 205). While some hero cults were begun in hope of gain, others were founded to appease a hero who had somehow been insulted and responded by sending famine or disease to a community. A well-cared-for hero, however, could provide any number of advantages to the community--good harvests, health to the people, and victory at war (Burkert, 206-7).
Asklepios' great popularity can, at least in part, be credited to one Telemachos, who took upon himself the responsibility of establishing a private cult to the god in Athens; very soon after, the Athenian state itself sponsored the cult, providing the god with temporary temple space in the Eleusinion (Garland 123) and later with his own temple. The perceived sponsorship of the new arrival by Demeter and her daughter was surely a great boon to the growth of Asklepios' own cult (Garland 124); similarly, several of Asklepios' other temples had originally been devoted to Apollo and were at some point likely to have been shared between father and son before they were turned over to Asklepios alone (Garland 118). The Athenians were at that time recovering from a great and debilitating plague which had reduced their population by perhaps a third, and they had very likely exhausted all other spiritual options and were ready to welcome a kind god whose sole interest was the health and healing of humanity (Garland 131).
In Asklepios' temples, however, a sick person could seek health in a different and unusual manner as well: incubation, in which the supplicant would spend the night in the temple, hoping for either a miraculous cure or (presumably more commonly) a dream directing him or her as to the best say to find that cure.(Burkert 215).
Often a person who sought healing from Asklepios would approach him with a promise, telling the god what he or she would give him once he or she was healed (Mikalson 23). When the healing had taken place, the person would give the god the gift in question, keeping the promise he or she had made. Again, this procedure was far from unique, and many or most of the offerings made to Asklepios were similar to those made to other gods in their own temples.
Most common were votive offerings of various sorts. While we may think first of the ubiquitous small terracotta votive figures, and these were of course very common, the size and value of the offering would depend on the financial status of the person making offering, as well as the degree of gratitude he or she felt toward the god.
Along with the terracotta figures, a supplicant on a budget could present the god with a terracotta or wooden plaque, to be hung on the temple walls or on nearby trees. These small plaques could also be made of more precious materials, gold or silver (van Straten 195-6).
Larger offerings might be attached to a pedestal, either on top if a statue or on the side as a stone plaque or relief sculpture (van Straten 192). A relief was likely to include an image of either the god in the act of healing the patient, or of the grateful recipient of healing making his or her offering to the god, perhaps accompanied by his or her family (van Straten 198).
Particularly interesting, and as far as I know unique to Asklepios, were the terracotta votive offerings, often life-sized, of parts of the body. These were not a universal phenomenon, and the type of offering varied somewhat with the region (for example, in Epidauros those who were healed would give an offering including a long, detailed description of the cure given), but in Corinth at least they were very common (Garland 123).
Asklepios welcomed offerings of many sorts, including cakes and other foods, and animals (a cock was common):
People in exchange for the fulfillment of their wishes could give and actually gave almost anything: money, frankincense, laurel, olive shoots, oak leaves, garlands, songs, branches, chaplets, pictures on which Asclepius was painted as well-doer...or brass rings..., candles..., offerings in gold and silver... Some patients even dedicated their sandals to the god; they had made a long trip in order to visit him, and thus it seemed fitting that they should give him their shoes. Whatever it was, the god received it graciously. (Edelstein 190)
Unsurprisingly, after a temple had been in use for a while, time during which votive offerings left for the god by grateful supplicants would have filled the temples to overflowing, something would have to be done to make room for new offerings. Rules set by the temples as to where offerings could be placed (van Straten 213) would have done little to help the situation, and certainly a restriction on type of offering would have been particularly inappropriate in a sanctuary of Asklepios. The offerings belonged to the god, so simply discarding them was not an option (van Straten 214). On occasion the more valuable offerings, those made of precious metals, were melted down to make something new for a temple, but the rules for this procedure were very strict (van Straten 215). It was also considered acceptable to bury, in a respectful and pious manner, offerings which were old or which had become damaged (Price 59).
Unlike many Greek religious practices other than mystery cults, the worship of Asklepios was primarily for the benefit of the individual; although individuals certainly made offerings of their own, state-sponsored cults typically held festivals in hope of gaining favor for the city. By contrast, although the state recognized the need for a healing god and Asklepios' cult was state-sponsored, Asklepios was almost always approached by individuals (Garland 134).
However, although he was most commonly approached by lone men and women seeking aid for their own needs, Asklepios' festivals were the work of the state. In Athens he had two. One, the Epidauria, was held during the month of Boedromion, in the midst of the Eleusinian Mysteries (not only had Demeter shared her temple space with the healing god at need, she shared a place in her most sacred festival as well):
The advent of Asclepius was worked up into a myth which told that in his own lifetime on earth Asclepius had come to Athens to seek initiation, but had arrived too late for the preliminary ceremonies, so that they had all to be rushed through again for his benefit on this, the fourth day. His privilege provided a mythical justification for any other would-be initiates who had started belatedly on the ceremonies. (Parke 64)The Epidauria included a procession, offerings and a feast (Parke 65)--in other words, nothing atypical for a festival.
His other large festival was the Asclepieia, held during the month of Elaphebolion, within the City Dionysia. Little is known of this festival apart from the existence of a good-sized sacrifice, and presumably a feast to follow. Although Parke does not give evidence of a direct connection between Asklepios and Dionysos, as he does with regard to Asklepios and Demeter to justify the placement of the Epidauria, he does wonder whether in fact some link does exist and finds it suggestive that one of Asklepios' proponents was the playwright Sophokles.(Parke 135).
However, I think it is more likely a function of the difficulty of adapting to a polytheistic religion--there are so many gods, and some people may prefer to limit the number they have regular personal dealings with. It seems to be much more common for someone in need to seek help with issues of health or healing from Apollo, and certainly as a god of purifications he is qualified, although historically he seems usually although not universally to have been more concerned with larger health issues--plagues and the like--than with individual needs. Additionally, there may be a question of whether Asklepios does in fact exist as a separate entity, or whether he is an aspect of Apollo. Finally there is Asklepios' narrow focus--unlike many of the gods, possessors of rich mythologies and multiple functions, he seems to be fairly single-minded, and some may equate that apparently narrow range of interest with the tendency in the later part of the era to deify concepts such as victory (Nike).
The polytheistic view of deity is one that perceives the gods as specialists. This doesn't mean that the power or ability of the gods is limited--if asked, and if amenable, any god can do any of the things we ask of them--merely that they are individuals with individual preferences and interests. For example, you could ask Athena for help with your love life, and if you have a good existing relationship with her she may well lend a hand, but her approach will certainly be different from that of Aphrodite, for whom those matters are far more of a priority. Asklepios is a healing god. That is what he does, that is what he likes to do.
He is also a responsive god, with an interest in the good of humanity. In my experience, Asklepios listens to sincere prayers and is more than willing to lend his abilities to those in need. He doesn't generally deal in miracles (although I certainly would not discount the possibility) but will support any efforts the person asking his aid makes on their own behalf.
The custom most strongly associated with Asklepios was incubation, sleeping in the temple in hope of finding a cure through dreams. Someone who is seeking Asklepios' aid might be advised to take particular note of any dreams he or she may have.
An offering to the god would also be a possibility. It was customary to give a thank-offering after the cure had been given; however, the timing of the offering could also depend on the type of offering being given, the nature of the help asked for, or of the ailment itself. In addition, the post-cure offering presupposes an ailment that can be quickly cured, and if you are asking for help with something chronic, or less cut-and-dried, you may want to give your offering after some improvement has been shown even if the ailment is still present to some degree.
Asklepios welcomed all sorts of offerings, so there's no need to be anxious about your choice. Traditional votives are appropriate, as are more seemingly-modern offerings such as candles and incense, perishable items such as food and flowers, and immaterial ones such as prayers and songs. In fact, this article you are reading right now is a thank-offering to Asklepios.
If you do choose to make a traditional votive offering, there is a wide range of possibilities; however, one type particular to the worship of Asklepios is the terracotta model of the part of the body you are asking to be healed. While making a life-sized model may be beyond our resources, a smaller one is far simpler and may be made of either oven-dried or air-dried clay without much difficulty.
Another consideration, and one to take into account while choosing the type of offering to make, is what to do with the offering once it is made. Songs and prayers, of course, will not be a problem for most people. Perishable offerings can be left on one's home altar for an appropriate length of time, which will vary with one's circumstances (for example, if you have house pets, you may not want to leave food offerings out for very long at all); if this is not possible, they can be left outdoors. More permanent offerings can also be left on the altar--indefinitely if an altar item or if you have room, for a shorter period of time if not. There is also historical precedent for burying these items if and when you are no longer able to keep them there.
Finally, you will want to consult your doctor or other health care provider in addition to any prayers or offerings you give to Asklepios. Asklepios, father of physicians, is most likely to help those who also take steps to ensure their own health.