Copyright

I'm starting a band, and want to cover a song (Strawberry Fields Forever, if you're wondering) and I'm wondering about how copyright laws and such effect covers.

If I want to cover a song (That song, or others, for future reference) what degree of permission do I need to get?

Also, I have google searched and such and know that you need special permissions and such to record and/or release covers, but I'm wondering about just playing them at a show or something.