Last weekend, I was hanging out with family, and my cousin said she'd been under a lot of stress. I recommended meditation, and she asked for instructions. These instructions are for her, and anyone else who doesn't know anything at all about meditation. I'm not a very experienced meditator, and I don't even claim that I really know what I'm doing, so take all of this advice (as you should anyone's advice about anything, really) with many grains of salt. If you already know how to meditate, this post is unlikely to have anything of value for you (but feel free to read it anyway). Moreover, I don't really know what I'm doing; I'm hardly an expert at this! I really like this website for more detailed intorductions.
There are many, many kinds of meditation. I mostly do a kind called "vipassana" or "insight meditation". I do some other things that are called meditation, but aren't exactly the same kind of "quiet the mind" meditation. For example, I've recently been doing something called "metta (compassion) meditation", which I also recommend, but it hasn't (yet) been shown to have the same kind of psychological and physiological benefits as "regular" meditation. When I was about 16, I read a short book called The Way of the Pilgrim, about a Russian monk learning to "pray ceaselessly". While (especially then) it was too Christian for me, it teaches a really effective form of meditation, which, it turns out, is VERY similar to the methods advocated by Abraham Abulafia. I'd strongly recommend it to Christians, but it's good for anyone who can choke down the Jesus. You can read it here (or in Russian).
So, here's how I meditate: First, find somewhere comfortable to sit. I meditate sitting straight-backed in a regular chair (because of my bad hip) but most people recommend sitting cross-legged. Set a timer on to ding twice, once after 5 minutes, and again after 15 more. If you're somewhere noisy, use headphones and white noise. Stretch a little bit, and make sure you're comfortable, then start the timer.
For the first five minutes, don't meditate, rather just let your mind wander. I find this helps to "shake out" whatever is rattling around in there. During this time, breathe deeply, in through your nose and out through your mouth, with a noticeably pause in between each. In, hold, out, hold, in...
After the first "ding", begin to focus on your breathing. While breathing in, focus on the feeling of your chest and abdomen expanding, filling with air. While breathing out, focus on the feeling of them falling back in. I find it helpful to think the word "expanding" while breathing in and the word "contracting" when breathing out.
Try it right now: Take a deep breath in, while thinking only the word "rising", wait a moment, and then breathe out, thinking only "contracting". Imagine you are a spirit, and have only recently come to be in this body. This is your first breath. Really pay attention to it, experience what it feels like to breath as if it new. That's all there is to it. Do that, over and over. As you get better and better at staying focused, be sure you're focusing on the actual rising and falling, and not the label.
If you notice yourself thinking something else, just calmly return to thinking about your breath. You just succeeded at meditation! The goal (at least in the beginning) isn't to not get distracted, it's to NOTICE that you're distracted. But, what if you can't "just calmly return to your breathing"? What if you're really distracted, or the distraction makes you want things or fear things, or feel sad or angry or whatever?
When that happens (and it probably will), think the verb you are doing "itching", "hurting", "worrying". You don't need to be precise (in fact, it might be better not to be). You can just think "knowing" or "feeling" or such. If the desire to scratch (or move, or whatever) is strong, you might think "wanting".
If you're having an emotional thought, which I find to be the hardest to let go of, remember that the goal is not to suppress or eliminate thoughts, it to let them pass through you without disturbing you. At first, you're like solid object; when a thought tries to pass through you, it hits you, and can hurt. Then, you become liquid; the thoughts pass through, but they leave ripples. Finally, you become completely ephemeral; the thoughts pass through you without any effect at all; they can't "get their hooks into" you.
If you have a severe itch or pain or a strong emotion, I find it helpful to focus my complete attention on that. Does your hip hurt? Think the word "hurting" with all of your mind, and you will find the pain start to melt away. Are you sad? Think the word "grieving" until that too melts away. When the pain (or whatever) has melted away, return to thinking only about your breath. Ideally, you want to get to the point where there is no distinction between "good" and "bad" thoughts or feelings, no distinction between thinking and feeling, where you are just "being". However, that takes practice.
If you get very distracted, focus on the distraction. The point is to focus, exclusively and completely, on one thing. It's not so important what that thing is.