Meditation is really just training the mind to concentrate on a specific point. It is often associated with Buddhism, but all the faiths involve meditation in some form (prayer is very close to meditation) and it is often practised by people with no religious affiliations or beliefs at all.

You can actually start straight away. For your first practice, all you need to do is sit still for 10 minutes, with your eyes either closed or looking at something very simple and relaxing, such as a single colour. You don't need to sit in any special posture at first or even be on the floor - just make sure you are comfortable. Then sit (you can have a timer on so you aren't tempted to keep looking at the clock) and just concentrate on your breathing. When you notice your mind starting to wander, just bring it back to your breathing. Really try to notice your breath as it goes in and out.

Once you've got the habit of sitting still and calming your mind, you can start looking at different ways of meditating as mentioned in the link above.