At it's roots, meditation represents a different state of being than the usual choices of aware/thinking vs. unaware/unthinking.
In meditation, we are aware/unthinking. With practice, it's benefits for both body and mind are truly impressive, but it's not an easy state to reach. The simplest place to begin is with your breath: count your heartbeats as you inhale through your nose, exhale through your mouth. Keep it simple, use the silent counting to distract your thinking mind while your experiencing mind just feels breath. Release any muscle tension that makes itself known. Depending on your heart rate, a 6 count in each direction is a good starting point, adjust up or down if you feel rushed or starved for oxygen.
Do this in a comfortable position, but without resting your back against anything. That way, you'll wake instantly if you start to doze. If you have a silent timer [no ticking sound, just a 'ring' at the end of the period], you can set it for 10 to 20 minutes, but be careful not to listen in anticipation of it ringing.
When thoughts come [and they will, don't be bothered], acknowledge them but do not welcome them or let them dwell-- dismiss them by silently asserting that these are things which can be dealt with when meditation time is over.
Try to get in no less than 10 minutes a day, everyday. You need that consistancy to begin feeling the effects and build the skill. As you get better at it, even 5 seconds on a noisy bus will rebuild your sense of calm, but if you ONLY do 5 seconds when you are particularly stressed, you won't find it useful enough to continue.
Check your local library or book store for 'The Mindful Way Through Depression': it has a lot of more advanced techniques, as well as some very clear explanations of depression, anxiety, and stress.