I am fairly new to FP as well, but in my experience I have found one of the easiest ways to utilize it (and practice) is to refactor old code-bases by breaking it up into pure functions that compose.
If a function does more than one thing (i.e. side-effects) break that up, and compose the resulting functions into a new function.
I realize this isn't a super helpful answer, but thought I'd try to help at least a little bit — I love the concept of FP, and I think just practicing and including it little by little is the best way to get used to it.