Picking a Star/DP

I got my instrument rating at an accelerated school in California.
Overall, I think my instruction went well, and I was very happy with
the results. I passed my checkride in a Piper Lance, and had no
troubles.

There was one part though that never quite made sense to me. My
instructor told me to use a Star or DP for an airport that wasn't the
airport I was flying to, and I genuinely had no idea how she was
selecting which one to use. At the time, I just fudged my way through
that, since my brain was approaching maximum capacity anyway.

Now I'm wanting to start filing and flying out of TKI in the DFW area,
and I have no idea how to determine which procedure I should file, nor
do I even see how the transition will occur from the procedure that is
routing to or from DFW over to a landing at TKI or takeoff from TKI.

Strange that I have this one gap in my training, but it's getting in
my way now. Can any of you clear this up or recommend a good book or
video that makes this process clear? And I don't just want to
understand the process here at TKI I need to know how to apply this
anywhere.

Thanks!
Bill
www.adventurepilot.com