I use debarbed or barbless hooks also for reasons stated by others, so removing a hook from me is not an issue. You just back out a barbless hook.
But I do want to recommend the method of removing barbed hooks as several contributors have discussed. I use to be an emergency room physician and have removed many a fish hook. I used a wire to put around the bend of the hook to pull the hook back out opposite to the direction it went in, but a strong string, mono, etc. will work just as well. Be sure what ever you use is strong enough that it doesn't break. Controlling the hook when you "snap" it back is necessary. You can simply push the eye of the hook to the skin as suggested by others before your short "snap," and this is usually adequate with small hooks to prevent them from turning (ie the shaft of the hook rises) and going in deeper, but the hook may still "go flying." With a single hook, I usually used a hemostat (something most fly fisherman carry anyway) clamped on the shank of the hook as near the eye of the hook as possible. I would press towards the skin with the hemostat and push the hemostat at the same time I did the "snap" with the wire/cord. It is a very short "snap" just enough to remove the hook which even with a large hook is less than a few millimeters. Teaching the patient how to do this to save an ER visit next time, took much longer than the actual process.
A treble hook or one of several treble hooks as often are present on many spinning and bait casting lures take a little more time as you have to be sure all hooks are under control before and during the "snap." The easiest way to do this is to use a wire cutter, if available, to cut off the "hook of interest" ie, stuck in the person leaving a long shaft. Removal is then similar to above for a single hook. I did wrap the entire lure in towels, etc. once to "save" a favorite lure for a patient, being sure that all none involved hooks stayed that way! However, better control is ideal.
This method is quick, easy, doesn't need local anesthetic, and can be easily done streamside which is much cheaper than an ER visit also.
Ideally wear glasses to protect your eyes just in case, but if done right, control over the hook is maintained throughout. Wash well with soap and water if possible. I never had any become infected, but I guess that is always possible.
Some ER docs still don't know this method, use local anesthesia, and do push the hook through the skin causing more tissue damage.
Sorry about the long post, but I hope this helps clarify the very simple method for hook removal that others discussed.
Remember to wear glasses fishing also, and have any children you take fishing wearing glasses. A hook in the skin is easy to deal with and doesn't cause much trouble usually, but a hook in the eye!!!
Rog