Surfing is a really cool sport / activity / adventure that can be very addicting. The adrenaline from catching a wave is unmatched!  
In general, you should know how to swim or tread water. You will get knocked off your board, and knowing how to keep yourself upright will make things a lot easier when you get back on your board to try another wave. Having great upper body and core strength will also help you with surfing. Next, you're going to need good balance too, so be sure to practice standing on one foot!
You do not have to be extremely fit, but the more in shape you are, the easier it will be. 
Finally, in order to actually be good, you need to practice, practice, practice.