My own personal exposure to category theory mostly consists of reading the following blog entries:
- The entire beginning of The Unapologetic Mathematician,
- Todd Trimble's series on basic category theory,
- Random weeks of John Baez's This Week's Finds (unfortunately it is somewhat hard to search these).
I won't claim that this is at all a systematic or comprehensive way to learn category theory, but I do think there's some genuinely good writing here and that it's gotten me comfortable with category-theoretic language, even if I wouldn't actually say that I "know" category theory (whatever that means).