You take it in, they check it for other damage besides the battery and if there is none then they accept it for battery service.
You do get a refurb, but this is an Apple refurb so while the internals may have been used before, the case will be completely new and I distinguishable from an off the shelf item.
US standard is $0 if you have AppleCare+ and $79 if you don’t, across the full range, but only as far back as the S2.
Add an extra $10 if you want the replacement shipped back to, it’s free to collect it at an Apple Store.