Place your cat on a table or hold him on your lap, or kneel down and clamp him between your legs. Grip a paw firmly and gently press on the pad to expose the claw. Don't forget to also trim the dewclaws that are further up along the paw. If you have a polydactyl cat, one with extra toes similar to thumbs, the claws in the folds between the paws and the "thumbs" also need trimming.
Using special clippers, trim off the clear, curved part of the claw in one rapid motion, cutting straight across and making sure to stay at least one-tenth of an inch away from the thicker part containing the vein, or "quick." When in doubt, cut off less claw and do the job more often. If you do accidentally cut the vein, stay calm. The claw will bleed, but your demeanor will affect your cat's reaction. Ideally, have clotting powder, a styptic pencil, cornstarch, or soft bar-soap on hand before you begin and apply it to the end of the claw. Or, you can press a gauze pad, clean cloth, or tissue over the damaged nail for several minutes until the bleeding stops.
Some cats (even first-time adults) will allow you to cut all their claws right away. For less cooperative cats, start by simply handling their paws more and more, pressing lightly on the paw pads to extend the claws. Once this is accepted, try clipping one or two claws, stopping and letting your cat go whenever he starts to resist; eventually, you will cut them all. A team effort may be necessary to contain a writhing cat, with one person firmly grasping the loose skin at the scruff of the neck or holding the cat wrapped in a towel with just one paw at a time free, leaving the second person to handle the task of clipping.