I do Theravada Buddhist medition.
I generally start off paying attention to how my body, or some part of it, feels. This has a calming effect. When I feel I’m ready, I move to concentrating on the breath. I usually don’t count, and I definitely don’t try to influence how I breathe. It’s kind of hard not to somehow influence it when you’re paying attention to it, but you do get to a point where it’s just happening.
You can pay attention to the breath in a number of ways. Most are very consistent in this, but I’m not. Sometimes I pay attention to it entering and leaving my nose, sometimes I pay attention to my chest, sometimes my belly. Depends what feels easy at the time. One should never try to visualize it, though; just experience it.
After about 20 minutes of just watching the breath, I usually move to Vipassana meditation. This is paying attention to what occurs, but not giving any thought to it. When you hear something, you just mentally note “hearing.” When you find yourself thinking, you note “thinking”. Thinking, as an activity, is not given a whole lot of weight; it’s just what the mind does, just as hearing is what the ears do. You also note whether a feeling (physical or emotional, but mainly the former) is pleasant, unpleasant, or neutral. When nothing seems to be going on, go back to the breath.
Sometimes I do meditate on an idea. For example, there’s a classic meditation that revolves around the idea that I will die, the time of my death is unknown, so what do I do. Or I may meditate on some idea central to Buddhism, like that of impermanence, non-self, and suffering. Another thing to do is a body sweep, concentrating on the parts of your body from the head to the feet, and back up again (slowly or rapidly).
Then there’s walking meditation, where you walk back and forth, just paying attention to the steps you’re taking. Most, including me, have a hard time with this, but I find it very beneficial when I do it.
Meditation works slowly on the individual. You won’t “get it” in a week, or even a month. You can’t really understand it unless you go on a retreat where you do it intensively for a day, or preferably several days. Over time, though, it changes you. It becomes something that you do, to a greater or lesser extent, much of the time, not just when you’re sitting on a cushion or bench.
I think it’s important to get a good teacher to get you started, but stay away from people with grandiose claims (anything having to do with Maharishi Mahesh Yogi is to be avoided, IMO). As mentioned, there are also good books. Joseph Goldstein, Jack Kornfield, and Thich Nhat Hanh are particularly good authors on the subject.
Hope this helps.