Buying A Horse
On this page, you can find information on how to buy your horse, from where to go, to the final vet check.
O.K., so where do I look?
When you are looking for a horse, there are several sources you can go to.
Brokers
Brokers are usually a good source because if they sell you a horse that is far more green than the broker told you, they get a bad reputation.  They don't want that, because most people find brokers through word of mouth, not through a phone book or at the local mall.  If this is your first horse and you don't know where to find a broker, ask an experienced horse person, like your riding instructor or the owner of a well known tack shop.  When you go to the broker's stable, look at the facilities.  Are the horses happy?  Do they look too thin?  How do the horses handle certain situations?  How does the broker handle the horses?  Is it a gentle or harsh manner?  These are all important questions.  If one horse can't handle being in the wash rack without freaking out, but the rest of the horses are calm, then it's probably not the brokers fault, the horse just probably was scared of the wash rack before it got into the broker's hands.  If most of the horse's are frightened in this situation, though, it is probably because the broker doesn't handle the horses in a gentle manner.  If you like the facilities and the horses, go ahead and look at the horses at the stable.
Private Owners
If you're looking through the Sunday paper and you see the perfect horse, it might be the equine pal you are looking for.  But, don't be fooled.  If an ad says "bomb proof," is it really safe in all situations?  Also, if the ad says "great prospect" or "great potential," what is that supposed to mean?  If it says "great hunter prospect," how high can it jump?  And who's to say that this horse has great potential?  If some famous horse trainer says it has potential, then it's probably true.  But if a person who doesn't know that much about horses says it has potential, how should they know?  If the horse looks to you like it has potential, then look into the horse more.  If your horse is used for jumping or other more risky riding, have the owner of the horse take the horse through the course before you even get on.  If the owner says it can jump 3'6", have the owner take it over a 3'6" course before you give it a try.  If the horse can't really jump that high, then it would be the owner's fault if the horse is injured, and if they seem hesitant, they might not have ever jumped the horse that high before.  Once you have ridden the horse, put it in situations it would have everyday, like a wash rack, picking it's hooves, tightening the girth, and leading.  If your horse is an excellent mount, bring your riding instructor or someone else who is good at confirmation and health problems to come check out the horse for themselves.  If they can tell right away that the horse has a problem, look at a different horse.  If the horse looks okay to your instructor (or whoever it is) than go ahead and get the vet check on the horse.  (Having someone else check it first will save you and/or the horse's owner the vet bills.)  If the horse is in good health with no major problems, then ask if you can take a trial with the horse, either at your barn or the owner's barn.  This way, you can put the horse in all the situations if you forgot to do this earlier.  If they are hesitant, say you will keep it at the owner's barn so that they are still in control of the horse.  If the horse lives up to everything you want in a horse, go ahead and write the check, providing that you have already purchased ALL of your horse's necessary supplies. 
Auctions
I don't reccommend auctions because you usually can't ride and spend a lot of time with the horse you are considering.  If you are very experienced and you know what to look for in a horse, like confirmation, then be my guest, go to an auction!