I’ve seen 1800s era dental tools and if I needed a tooth pulled id just get a wrench or pliers my self …
But we were watching some version of the old ok corral and doc holiday was in it and we started talking about dentists back then and It seems that 1 almost anyone could call himself a dentist and 2 they seemed not to know much other than pulling teeth (maybe because what counts for modern dentistry came about in the 20s or so ive been told )
How limited were they actually ?
Archeological evidence suggests that people have been replacing missing teeth for a very long time, with at least as much success (the patent surviving and thriving) as trepanation.
Now, applying directly to US Old West, you add also the economics of how remote these locations were, and what people living and working there can afford. So maybe you want a more local historical reference. But yeah, there’s plenty for the dentist to do.
Treating gum abscesses and such would have been common.
I got one as a kid. The dentist just swabbed it with something and popped it with a sharp probe. No further problems.
An old timey dentist would have swabbed some alcohol or some such on it and popped it.
More serious abscesses would need more treatment. Poultices and the like would have been popular.
A sharp edge from a chipped tooth could be filed smooth with simple tools.
Yeah they could give you a haircut too. 
The Sydney Morning Herald of 1 Aug 1842 advertised a French dentist who had just set up shop:
*Mr. J. EMANUEL
Surgical and Mechanical Dentist.
BEGS to inform the gentry and inhabitants of New South Wales, that having arrived from Paris, he intends practising as above.
Mr. E. proposes introducing an entirely new method of stopping decayed teeth with his
NEW PREPARATION OF GOLD,
which from its durability surpasses all other metal. This is applied without giving the slightest pain, prevents further decay, renders extraction unnecessary, and removes that unpleasant odour in the breath invariably accompanying decayed teeth.
Mr. E. likewise supplies deficiencies of teeth in a very superior style, and in every case restoring perfect articulation and mastication. Loose teeth fastened, whether arising from neglect, the use of calomel, or disease of the gums.
Mr. E. extracts all kinds of stumps with the greatest facility, also effectually cures the most acute and complicated diseases appertaining to Dental Surgery.
…*
Other advertisements mainly dwell on supplying artificial teeth. I guess any bozo with pliers could yank out a tooth, but its getting a decent quality replacement set that lets you maintain your lifestyle is where the professional effort would be.
My grandfather was an amateur dentist and left behind a nice variety of dental hand tools, many of which I still have. In his heyday it apparently wasn’t that rare. He lived 1890 to about 1964. I knew him but he didn’t work on my teeth.
The titular dentist in McTeague (1899) mentions doing a dental bridge for a customer. He eventually gets a cease and desist order from the County of San Francisco for practicing without a license, since he had learned by apprenticeship, as a trade.
Speaking of McTeague, do they still teach it in high schools? I never had it assigned to me, but I frequently saw schoolmates carrying the book around.
Book I’m reading (The Sisters Brothers), the dentist extracted 2 teeth and even gives a toothbrush with tooth powder to the brother. But it also mentions that the “dentist” just sent away for the tools and didn’t actually go to school.
Certainly there were false teeth before then, even George Washington had a few. But I do wonder how many practicing dentists actually had any training.
Fun fact: Doc Holliday went to the first dental college established in the US . It was located in Baltimore.
According to what I’ve read, he actually was a pretty good dentist, in the modern sense. Made nice bridgewark and stuff.
He was just better at…other things.
“I’ll be your huckleberry.”
I once saw what was claimed to be George Washington’s false teeth. They appeared to be wood. They were in a vault at the NY Academy of Medicine (5th Ave. and 103rd) so have some chance of being real.
If they were wooden, then they weren’t Washington’s.