Meditation is something which I'd always been attracted to. A long time ago I felt that if there was another dimension to life, it wasn't knowable from normal states of consciousness. That the only way to know if there was something more than the perceivable/scientific world was to undertake experiments with consciousness to gain direct experience.
So I've dabbled in many forms of meditation. The one I did the most was from the Brahma Kumaris Society. As far as religious people go, I think they are about as good as it gets. They offer most of their teachings for free, aren't too dogmatic, and if you just want to learn how to meditate they won't try and brainwash you, or that was my experience anyway.
I did two courses with them, and had the picture on the left on my wall for many years. Perhaps you can do what I did then, stare at the centre of the picture, relax all the muscles, especially the ones around the eyes and forehead, and think of a dark infinite space in which you are gently floating towards a cool, loving light. They have tapes and other things to lead you through meditation, which probably won't be anything like mine. I got more interesting experiences from other forms of meditation, but the daily meditation I did with Brahma Kumaris did seem to still my mind. I didn't get songs stuck in my head, thoughts which had previously brought back strong emotions I was able to look at in peace, I was able to still the thoughts in my own mind long enough to really listen to other people.
So my advice, take wisdom where you find it, but as always follow your own path, even if the path you are being lead on is as gentle as the one trodden by Brahma Kumaris.