You Need to See the Horse
You need to see the horse without any tack on, and with no bandages or boots on its legs. Assess the conformation, looking to see if it has any major conformational defects — your knowledgeable friend could be useful here.
Feel the horse's legs D see if it has any lumps, bumps, or heat that should not be there. Pick up all its feet in turn. (Always exercise caution and good sense when approaching an unknown horse.)
Ask to see the horse run up, that walked away from you, and trotted back toward you and past you. Assess the horse's soundness, and also look at its action, i.e., is it very close in front or behind, and does it move straight?
If you still like the horse, ask tî see it tacked up, and observe how the horse reacts. Does it object to the saddle being put on, etc? This can give you another clue to its temperament.
It is generally normal practice for the person selling the horse to ride it first. Observe how it goes, and then if you still like it, ask to ride it yourself.
You should try the horse at all paces, and also try jumping it. You should also consider riding it up the road. By now you should have a good idea as to whether or not the horse will be suitable for you.