To actually learn it, Mac Lane & Saunders "Categories for the Working Mathematician." seems to enjoy continued popularity.
I actually found MacLane's book to be more approachable than Awodey's. Although I'm not sure this is good advice because it took me several years casually feeling my way through the field to start to gain an understanding into it (ie YMMV).
Interesting category theory historical fact! Checkout MacLane's wikipedia page and you will find one of his students was in fact Steve Awodey.
This is the best way I've found so far, and I had been semi-supplementing with MacLane and Birkhoff's "Algebra", just to get a feeling for the vocabulary; bringing myself from the space I typically mathematically exist in, to the space of category theory. Nothing else really has come close in composing the correct thought direction. It is dense, but I enjoy it very much. It is very beautiful math.
By the way, it's not two authors; the single author's name is "Saunders Mac Lane".
There he also lists some books on category theory. I am putting a direct link when he mentions the references.