I started the search for a non-religious meditation technique four years ago. In July 2009, I did my first course of Vipassana -
http://www.dhamma.org/ . Since then I am doing it.
My life has changed a lot since then. I would really recommend you to try it out. You don't have to believe in anything to start with.
The basic course is of 10 days spent learning the meditation in a centre. You will get the details on the website.