There are many methods being used at this time. The two most popular is a method of actually casting or tossing the runes on a cloth or table of some kind and using the runes as they surface face up to tell us things. This is a great method, and is used by a lot of people. The difficult aspect of this method is knowing what positions may mean, proximity to other runes, and what they overall shape may indicate. I have found that this method is much like divining from tea leaves or ashes, though it is a bit easier because the runes give us a few more concrete things to hold onto. I have found this method works well for deep trance workings and intuitive casting. I also suggest that if you are new to divination, you may want to wait on this casting form until you feel very secure in your abilities.
The other most common practice is very similar to tarot layouts, where one uses a layout to perscribe meaning based on specific positions. Of these the most common is a three rune spread, often equated with the three Norns, the first rune representing that which is, the second that which is becoming, and things which may come to be. Other more involved spreads are available. Freya Aswynn lists in Fruits of Yggdrasil a nine rune spread which corresponds to the nine worlds. I have found that this method(the placement method as a whole) works well for specific questions, and can aid a great deal if you find yourself doing readings for people you do not know and cannot seem to connect with.
As for how to learn divination techniques, that is simply a matter of practice and divination. After you find you have learned some things about each rune, one can start by pulling out a single rune each day and asking it what the day may bring. Start to find correlations between the rune you pulled and events of the day. This is an excellent way to begin making everyday associations with the runes. On the whole, like with everything else in life, it is a matter of practice, practice, practice.
At this time I am not posting my meanings of the runes, as I think it is most important for you to find your own interpretations. I would suggest doing so by meditating on the runes each day in a manner fitting your own style and practice.