Farriers just do feet, and 98% of the time they come to you.
The teeth thing is a BIG can o' worms. Vets would like you to believe that only vets can do teeth, and that they do it well. In reality they get next to zero instruction in it in vet school, and often don't learn much of anything more after that, and a great many vets SUCK at floating teeth. (A few have the sense to realize that, and just won't do 'em). IME it is *hard* to find a vet who is actually good with teeth, especially on a horse with a not totally average problem-free mouth.
There are some vets who specialize in dentistry. Many of them are actually pretty decent IME. Not all of them though. Price is no predictor of ability.
In most places there are also non-vet horse dentists. Some of them are a MENACE. Some of them are well intentioned and harmless and no worse than yer average vet. Many, IME, are really pretty good. However the veterinary community seems to view this as a horrible threat and/or affront, and has launched some very hard-nosed take-no-prisoners steps in certain regions to totally shut out all non-DVM practitioners from working on horses' teeth in any way shape and form. (In other areas, a truce of some sort exists, often with the better 'lay' horse dentists having a working relationship with a vet so that the vet will come over and do tranquilizers etc when needed)
For getting teeth done, I have paid as little as $45 (for a vet, plus farm call of course; and also for a lay horse dentist who was EXCELLENT with the horses but not so brilliantly thorough with their teeth); and I have paid as much as $400 for two horses (for a specialist vet, who did a pretty good job but I'm not convinced any better than some other floatings I've paid considerably less for elsewhere). So, it's complicated.
Mostly they come to you; sometimes you trailer the horse to the vet's clinic but that can get kind of complicated and lengthy if the horse is tranquilized as is very commonly done.
It is ABSOLUTELY worth having any new horse floated by someone GOOD; also any horse should be checked and probably floated at least every few-to-five years, more often if there is a behavioral or digestive problem or if you know the horse has recurring teeth issues.
Pat