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https://palousemindfulness.com/ may be worth looking at to start. Its a free course with plenty of explanatory text/ lectures, based on jon kabat zinn's approach - so largely "non-religious" meditation, with a focus on practical benefits and free from the pseudo-spiritual stuff that dancing james refers to
Another thing to look at is Geoff Hunt's new buddha way, based down at surrey university: http://www.newbuddhaway.org/meditationsessions/howtostartmindfulness.html Again not "religious" but focused on how these practices can be used to improve day to day living. I went to a beginner day with Geoff maybe 12-15 years ago - no idea if they still do them, but highly recommended as a way in if they do
So I have now done half a year of daily meditation with the headspace app. It has been really useful putting that little bit of structure into my days. Am feeling calmer, better focused and the courses have covered relationships, health, sleep, generosity etc etc. Though am now preferring to do longer unguided sessions.
They have sent me a code for 3months free access to the service. If anyone would like it and is likely to use it please drop me a PM.