Paolo Aluffi, Algebra: Chapter 0
Charles Weibel, An Introduction to Homological Algebra
Kashiwara M., and P. Schapira, Categories and Sheaves
These three are roughly ordered in terms of terseness. Aluffi’s text tackles some basic homological algebra in the ‘easiest’ case(namely where we have enough projectives or injectives), and is a fine introduction to cut one’s teeth on before moving on to something more complete.