I've been meditating for the past six months very regularly. It's something I regularly have to force myself to do, because to be honest, it's hard work. The point of meditation isn't to COMPLETELY empty your mind. That's impossible, because if your mind was completely empty, you wouldn't exist. (I'm currently studying in Buddhist traditions, particularly Zen, though I read a lot of books on Vipassana/Insight Meditation ala Jack Kornfield and Ajahn Chah.) But it would be correct to say that the point of meditation is to calm your mind down and reduce the mental chatter. That's accomplished through building your concentration and building an internal atmosphere that is gentle and forgiving rather than punitive.
In Zen as in most meditation traditions, you try to focus your mind on a single object. That object could be a mantra (
anything works, but in my school they use "clear mind" and "don't know" on the in-breath and out-breath) or the breath, or both. If you use a mantra, you can divide your attention by keeping 90% on your breath -- the sensations you feel as it goes in and out -- and 10% on your mantra, which will become softer as your practice.
The biggest obstacle you will encounter is distraction. The best thing to do for a beginner is to notice it, name it very softly (planning, worrying, doubting myself, pain, restlessness, thinking, analysis, anger, whatever's going on) and gently and smoothly move your attention back to your breath/mantra without making a big deal about it, i.e., without getting down on yourself. This process of naming is really an artform that takes practice. At first it's kind of clumsy.
This book outlines the process in greater detail and you should read it.
There are some other fundamentals, too. Posture is important. You want to find a posture that supports you for 20-30 minutes with minimal pain, but also maximum attention. You can sit on a chair, or a low cushion, legs folded across or under you. The specifics don't matter. The goal is more important. Also, you want to either close your eyes or keep them focused on the floor with the kind of gaze you would have if you were looking at someone you were really fond of.
The payoff...I can tell you from my personal experience that meditation is helping me choose when I react and when I don't. In situations where I would be prone to attack or defend, I'm now more likely to wait and assess the situation. Right after meditation, I can be very calm for hours. It's important, however, very important, that you don't sit with any lofty expectations. One lesson I've started to learn is that I'm okay where I am with my progress. My breath may not be very clear, and my attention still wanders like a motherfucker, but it's okay, and I can still focus on my breath and do my best. This goes back to what I was saying about not penalizing yourself for your lack of progress or skill. As soon as you do that, you'll notice some interesting changes that I'll leave up to you to figure out.
The greater benefits, which I have yet to experience, is an understanding of what you are, what exactly is the "I" or "me" that we refer to in casual speech, how to best help other people, and freedom from suffering (which is not the same as "pain").