Research lots!!!! It helps if before hand you lease a horse. Make sure someone who knows horses well is with you when looking like your trainer when your testing out a horse so they can tell you how you look
Have an experienced horse person with you. Ie, your coach/ trainer/ etc. They know what they are looking for (by this i andean any issues with the horse) and what would suit you best as a rider and your skill level.
Vet check with x-rays. You never know what you cannot see.
The first and most important tip I have is: Always get it checked by your own vet, depending on your purpose of the horse get it xrayed, and if the vet finds some flaws, look for a different horse. There are so many horses for sale, rather spend a little more money on a healthy horse than get a cheap one that takes hundreds or even thousands of dollars/euros/money on vet costs and little riding time.