It's late so I'll keep it short, promise. :)
Astral Travel is not necessarily a spiritual concept, spiritual refers to anything working with or on higher power, enlightenment, ego, afterlife, spiritual religion, etc...
Astral Travel can be seen as a very scientific theory regarding the splitting of your conscious. There are different ways to look at it, there is the subtle body theory, there are several more spiritual theories, and there is hypothetical remote viewing like concept...
Typically everyone projects one way or another. Astral projection (being one form of astral travel) is a lot more common than people often expect. You probably have successfully mental (another form) and astral projected at least a dozen times in your life mistaking it for a day dream, fantasy, or an actual dream.
I suggest just looking up different ways to project, trying the more basic methods and you'll eventually come to the one that really suits you.
My quick advice is to never push yourself too hard, so don't exhaust yourself. Travel is a very naturally occurring aspect and you shouldn't feel you have to strain yourself.
Get your rest, learn to relax, learn to focus, and learn to relax and focus simultaneously.