This is how to actually catch a wave. The way you take off can vary from wave to wave and is dependent on the wave type (shorey, sucky reef, point break, late take-off, early take-off).

how
You can catch a wave at any point - you just need to be going fast enough. As the maximum speed you can reach is limited you need to find where you can catch the waves. The criterior for being able to ride the wave is its steepness. The steeper the wave - the more it will push you along and the easier to catch. Look at where others are catching the waves, that should give you a good idea as to where you can catch the waves.
So you've selected your wave and are in generally the right position to catch it - turn around and paddle. Sometimes you'll need to paddle hard, other times hardly at all. Knowledge of this will come with experience.
You can use all three paddling methods but if you are only using your legs you find it useful to push down on the nose of your board to increase the planning speed.

tips
The angle that you take off can greatly effect the way you ride the wave. On fast waves like a point break it is an idea to takeoff on an angle to wave. For late drops, the drop needs to be straight down the wave.