I'd like to start this by saying, I'm no expert.  However, it seems likely that there are people who don't have previous experience meditating.  In light of the fact that this is a meditation forum, I thought a general intro might be appropriate.  So here's a (hopefully helpful) starter from my own experience.

When I meditate, I sit cross-legged on a cusion.  There are a couple reasons for this.  One is that it is more comfortable than sitting on the floor.  The other reason is that the slight tilt of the pelvis opens the abdomen and allows for easier breathing.  I also find that sitting and maintaining a good posture helps me to remain alert. 

This is where we get to the real meditation stuff.  Breathe deeply, allowing the abdomen to shape your posture on the in breath.  When you get your posture straightend out and you are well ballenced over your hips. . .  intentionally stop thinking about ANYTHING.  This includes the thoughts about not thinking thoughts about stopping thinking thoughts about not thinking. . . the easiest way to do this is to focus  on breathing. Count breaths to ten and then start over again.  with practice you will be able to shift your awareness easilly without all the counting and such, but it is helpful for a while.
 
I usually just breathe for a while with no thoughts, till I feel like I'm done. . .  But sometimes, (especially if you are new to meditating) it can be nerve-racking to loose track of time.  If you are doing it right this is EXACTLY what will happen.  The easiest way to keep this "time anxiety" from ruining your meditation is to set a timer.  Try for five minutes.  Try for ten or twenty.  Just do what is comfortable for you. 

There are so many benefits it's hard to even start listing them.  At the very least it will help release stress, which is a product of our over active thoughts.  With practice it allows you to gain control over your mind, and that can be most beneficial to people who want to have lucid dreams.

Any other input? or questions?