I'm assuming that you are wiring it up in your garage, but a little more information is required.
I think you mean breaker, not fuse since this is a 220V 15A compressor, unless you're in an older house that still uses fuses. First of all, you have to take into consideration how you are wiring it in. Is the wiring going to be in conduit, in the wall, etc? The wiring size will be determined by the load of the compressor, in this case 15A, but the wiring will have to be de-rated by a certain amount based on whether it will be in-wall, in conduit, normal ambient temperatures, and the length of the run. You will also need to verify that your panel can accommodate the additional load, and that there are additional breaker slots available if you haven't already done so. Once the wire has been sized according to the previously mentioned items, you can size your breaker based on the wire size. I am not a licensed residential electrician, but I have been doing industrial controls for over 10 years. I typically like to add an addtional 15% safety margin when sizing my wiring and breaker/fuse sizes due to inconsistencies in manufacturing. I would recommend hiring an electrician if you are unsure at all, nobody wants to risk burning their house down to save a few bucks. If you insist on doing it yourself, go to the library and check out the current NEC code book. It will have all of the necessary charts, tables, de-rating guides for each type of wire and installation application. Remember to also check out your local counties code regulations, you can usually find these online as well. This is important because some areas will often have additional requirements that are more strict than the NEC code and you don't want to have to deal with electrical code issues when/if you go to sell your house. Most home inspectors aren't intelligent enough on the matter to know any better, but some are and as a prospective home buyer, I would walk away from any home where I see obvious signs that unlicensed electrical work had been done.
You can do it yourself, but don't make any assumptions or cut any corners.