It is best to have your cat altered before they reach sexual maturity, some time between 6-8 months old. Both spaying and neutering are routine procedures. Of course, with any surgery there are risks, but they are relatively low. You may opt for pre-operative bloodwork which will pinpoint unexpected problems. For both procedures your veterinarian will have you drop your cat off early the morning of the surgery, and they should not have anything to eat after midnight.
Neutering is the term for the male cat's procedure.
Male cats are lightly sedated, and the testicles are removed from two small incisions in the scrotum. They usually do not require sutures, and will just have the incision area coated with an antibiotic powder. Barring any complications, they can go home the same day, and will be back to normal within 5-7 days. The only caveat here is if your cat has a retained testicle, then the surgery follows the same basic procedure as spaying. Spaying is the term for the female cat's procedure.