"I thought lock picking was illegal"
Lock picking isn't usually illegal. Let me make that clear, in some places it is illegal to use and/or own lock picks. But in a lot of places, at least in the US, it is not illegal to carry or pick a lock that you own. Also, common sense, but DO NOT USE/OPEN/PRACTICE ANYTHING YOU DO NOT OWN. More information can be found at the legal page.
Locksport
People that like to lock pick for a hobby usually call it locksporting to defuse the name of lock picking. It usually also refers to making so called "challenge locks" which are locks that are made to be a challenge for other locksporters.
Picking a Lock
Picking itself isn't too complicated of an idea, the problem is transferring it to hand movements, feel, and thwarting different ways lock manufacturers combat picking. Locks that are more difficult are more pick-resistant and have more things that try to trick you. Once you learn how each one of these "feel" then it can be pretty easy.
The basics of picking a lock, first you must have two tools, a tensioner and a pick. The tensioner should be in the bottom of the "keyway" or opening. Then you should slide the pick in and try to tap the pins in the top. The goal is to try to push the pins above the "shear line" where the "core" meets the outside of the lock. The tensioner should be used to put tension on the side you are turning the lock.
The first lock you should try to pick should either be a clear "acrylic" lock that comes with many beginning pick sets, or a common master lock. Master Lock is notorious for having bad locks, they do actually have a few decent ones, but most of their common ones are pretty bad. I suggest one of the models #1-#8 of the Master Lock brand.