What a problem subject.

The biggest problem people seem to have is that we are constantly told that "you must quiet your mind!"  You wanna know something?  This isn't going to happen.  We're not all Zen masters, and some of us just have a lot of trouble with not thinking.  So, instead of stressing yourself out over it, change your approach.  Don't worry so much about trying to force your mind not to think.

The method of meditation that I have found the most useful is not one of silence, but one of acceptance.  Best of all, it will make you a less tense, more relaxed, more accepting person.  This is something you will gradually improve at if you keep at it over time.

Remember, if you're starting out, don't meditate after a meal or when you're tired.  It isn't easy to practice if you're tired.  Sit comfortably, preferably with your back straight.  Now, pay attention to your breathing.  Don't try and control it, just watch it.  Don't judge it either.  Just sit and listen, feel, and so on.  It doesn't matter how well you're doing this.  If your mind wanders, bring it back to your breathing.  Do not get mad and think that you can't do it.  Just accept that your mind has wandered, and bring it back.  
The main idea here is to do this without getting frustrated.  No one is standing over you, judging you.  If you do get frustrated, accept the fact and let it pass.  The idea is to learn to accept every little thing about what is going on - whether your mind wanders, you start to get annoyed or frustrated, you don't think you're concentrating hard enough, and so on.  In the beginning, this can be very difficult.  If you manage to get through the initial stages, then you can go into focusing on other things like an image or a symbol, a sound, or anything else you can think of.  It will also make you more accepting of who you are.  Instead of getting angry, and being more angry because you don't want to be angry, you learn to accept your anger and where it came from, and you learn to let it pass.

Now, isn't that easier than being told straight out to "quiet your mind?"  Try this for 5 minutes at a time, and don't get mad at how it goes.  Don't even care about it.  Just tell yourself you're doing it to try it and it's no big deal.  After time, you will be able to focus more and more, and you may also learn things about yourself that you didn't know before.  Try it, and let me know how it goes!

Ok I thought I would add some activities which are helpful with and related to the whole "relax and clear your mind" thing.

This exercise is based on the concept of not knowing total relaxation until we experience total tension.
Lie down on a comfortable surface, on your back, with your arms at your sides.  Tense up your feet, hold for 5 seconds, and release.  Tense up your lower leg.. and release.. work your way up your body, continuing with your thighs, bum, abs, chest, shoulders, arms, hands, and head.  Once you have completed this, tense up your entire body.  Count to 10, and release.  Take a deep breath, and hold it.  Count backwards from 10, and at 1, release and relax your entire body.  Remember this sensation, and any that follow it.

This exercise is a way to help your mind to focus, and can follow with visualization.  Sit up straight, with your knees under you, legs crossed, or whatever is comfortable.  Close your eyes and take deep breaths, paying attention to your breathing.  After you feel relaxed, start to hum quietly.  Focus on this sound.  After a while, many will enter a trance-like state, suitable for visualization, which is another lesson.