Most folks these days ride with a cleat (a metal piece) that is screwed to the sole of their shoe. This clips/cleats into a pedal which has a spring-loaded catch on it. These pedals are usually pretty small and consist mostly of the cleating mechanism but can have a platform built around it. You cleat in by stepping on the pedal. You get out by rotating your heel outwards.

The more traditional approach (pre-Greg LeMond fame here in the US) is a cage and strap. You have just a traditional pedal (platform) to which is attached a cage that only goes around the front half of your foot. A strap is threaded from one side of the pedal through the middle point of the cage to the other side of the pedal. You pull on this strap to release it. The thing is you have to bend down to loosen it also.

Maybe someone has a picture of the strap/cage combo they can post. If not, I'll do a little sleuthing.