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Category theory on its own can appear very sterile and for good reason. Many of its concepts subsume and unify quite a few constructions in many other settings so a single definition "means" more in category theory than the same definition properly interpreted in some other theory. The others have already mentioned this but the best way to learn category theory is to pursue its development in a setting you are comfortable with. The current trend in graduate algebra books is to introduce categories quite early and use it as a guiding principle and unifying language for the development of the various algebraic theories. A favorite of mine is Paolo Aluffi's "Algebra: Chapter 0". My initial attempts at learning category theory failed miserably because I just stared at the diagrams hoping they would start to mean something so don't do what I did. Whenever you come across a definition or a diagram try to see what it means for sets and maybe one other algebraic category like rings or abelian groups, in fact the more you develop your set of examples the more you will appreciate the unifying language.