Same with yoga, there is no connection to any particular religion. It is just about stilling the chatter of the mind and reconnecting with the true self within. A really simple but effective technique that I teach is to breathe naturally but to focus on the pauses or spaces between the breaths. With practice the pauses between the breaths can be lengthened and it is there that you can glimpse that perfect absolute stillness of mind. Can be done anywhere, anytime and is really easy to do.
I teach nature meditations too with the aim of re-establishing our dwindling connection to the natural world. Tom Brown Jr students will recognise this technique as 'sit spots'. Just find somewhere in nature to sit, against a tree is always good and focus all of your attention on the immediate area around you. Let go of any thoughts and just breathe and allow all of your senses to take in the sights, smells, sounds in the vicinity. This technique is usually used in order to reduce your 'presence' in the woods and bring the wildlife closer to you as well as to sharpen the senses, but it is also a great meditation practice in its own right. Just try not to become involved with the thoughts that pop into your head, be an observer of them instead, notice they are there and then allow them to drift away again. Bringing your focus back to the breath is a good way to achieve this.
There are loads of other methods from various angles but essentially the key aim is to still the constant chatter in our heads (monkey mind!) and get a glimpse of perfect peace - the feeling you get when you see a beautiful sunset and there is nothing in that moment except the beauty of it.
What a hippy I am!!