How to get rid of black dots on hardwood?

Doesn't look like oak to me but I'm not a pro. The dots are small holes in the wood filled with stain. You'd have to sand the table down beyond their depth but when you refinish it, you'll have the same look. Maybe wood isn't the material for you. This is what wood looks like.

Are they on the legs as well? If so, pick a spot you can't see, and get at it with an exacto knife to see how "deep" the dots are. If you can cut them off (as in, they're superficial), you have a chance of something being able to clean them off. If you can't cut them off, then they're inside the wood somehow.

I think it's quartersawn red oak. It's possible that the dots are actually in the finish rather than on the wood. Like others have said, the only way you'll know what they are is to sand off the finish in an unobtrusive place and see what you have. Underneath the table is a good place if the spots are there. If it is just the finish, then sand it down to bare wood and refinish with whatever finish you prefer

Hmmm... In my case my table has similar black dots, but they are by design. It's quite possible your's is the same, that it was intentionally "distressed" to look that way. This is quite a popular look for some customers.

For mine, it's not just dots though. It's dots and divots and straight depressions etc. The carpenter accomplished this by whipping the table-top with a thick chain, then staining the entire surface, and then sanding down the black top surface, leaving the black stain in all the natural crevices and artificial depressions. Then it was varnished on top to protect the black stain and the wood.

https://www.younghouselove.com/how-to-distress-wood/

Alternatively, I wonder if s/he might have flicked stain onto the table top after the sanding?