Check horse against passport, age, look in mouth, check eyesight, walk and trot up to check for abnormalities in action, flexion test (optional extra), a quick check of spine and legs (reaction to pressure, checking for splints)... can't remember much else.
Basically check it is the same horse on the passport, of the right age, that the eyes are okay and that it isn't too lame for light work.
I think it varies a little between vets, though and some optional extras can be added (like blood testing so you could later prove the horse was doped when vetted).
The horse I had vetted failed on flexion - my trimmer had already warned me there was a problem. Next time I will listen to the first expert before paying for the second!!
I didn't get the current pony vetted... I was still smarting from the failed vetting - so far, so good!
Depends on what the client wants and what the vet thinks to some extent. The last pony I sold that was vetted was supposed to have a two stage, but was subjected to repeated flexion tests as the team of vets, some of who were vets for the last Olympic teams, couldn't believe that an older pony could possibly be so sound. They hardly managed to make him take a lame step between them, which I suppose went to justify the high price asked
Having recently been a purchaser all the owner can do is be honest and polite. The owner of the horse I had fail was mortified - she really thought she would pass and was so sorry I parted with 220 for absolutely nothing... but hey, it's not money wasted - I might have saved thousands in vet's bills!
Personally, I found the whole thing nerve racking as I really wanted the horse badly - the owner really wanted me to have her, too, so it was a gut wrenching experience for everyone.