Read the first chapter (not more, since then the book gets a special bias) of [Barr/Wells][1]. This leads you in a very short and straightforward way through all basic concepts. The exercises are many, easy and illustrative - do a lot of them, and always try to see what the notions mean in other settings you know.

Contrary to many suggestions this would mean to start by studying pure category theory. But not for a long time, since the text is reasonably short. I found it good to go through the first few basic concepts at once, since together they make more sense than individually. Some examples are provided in the exercises, but after this try to find more sophisticated examples in fields you know...


  [1]: http://www.tac.mta.ca/tac/reprints/articles/12/tr12abs.html