You need to figure out which breaker controls the outlet, then determine the wire gauge, probably by opening up the outlet box and breaker panel and measuring. Ideally, you want 6 ga for a 50A breaker (charging at 40A, always 80% of the breaker max). Depending on the type of wire, 8 ga could work, if the whole run is in conduit. If the wire is too small, you can either (a) replace the breaker and outlet with a smaller one to match your wire, or (b) upgrade to heavier wire. Again, if it's conduit the whole way to the panel, and it's big enough, pulling new wire should be easy.What would I be looking for in terms of wire (size?) and breaker?
You need to get an electrician involved. To do it right, there's non-trivial stuff here (conduit fill calculations, etc) that you should leave to a pro, unless you really know what you're doing.