Every pedal fits into every crank arm thread, but there are exceptions such children's bikes and some old one piece cranks.

There are two main types of pedals, clipless and platform/flat pedals. For clipless pedals the shoes need to have cleats screwed into them to click and attach to the pedal, depending on the type of clipless system you use will dictate which shoe you need.

The two common types of cleat attachment for clipless pedals are SPD, which requires a two screw system and the SPD-SL, which requires a three screw system. There are other systems, but they will use either the two or three screw system to attach to clipless shoes. 

For platform pedals, you can use any shoe you are comfortable with.