If you look around the salon you will see the sterilizers and you will see them using them. They are required by law to do that. I used to get my nails done 6 months of the year for about 6 years. (I stopped because I was ruining my nails, one doesn't grow right anymore - it's flat on one side and bent somehow- and they got real thin) So if you get nails done, don't do it too often due to that.
And if you like getting them done AND are worried (I know that no amount of reassuring will help) then you can bring your own little sander thingie (Sorry, don't know the technical name for those things! But I'm talking about those little round things they put on the end of that grinder thingie - LOL! - and they look like they are made of sandpaper) also your own file, etc.