Kapustin-Orlov'a survey of derived categories of coherent sheaves is pretty good,

• A. N. Kapustin, D. O. Orlov, Lectures on mirror symmetry, derived categories, and D-branes, Uspehi Mat. Nauk 59 (2004), no. 5(359), 101--134; translation in Russian Math. Surveys 59 (2004), no. 5, 907--940, math.AG/0308173

but more slow/elementary exposition starting with fundamentals of derived categories is in an earlier survey of Orlov

• D. O. Orlov, Derived categories of coherent sheaves and equivalences between them, Uspekhi Mat. Nauk, 2003, Vol. 58, issue 3(351), pp. 89–172, Russian pdf, English transl. in Russian Mathematical Surveys (2003),58(3):511, doi link, pdf at Orlov's webpage (not on arXiv!)

There are also Orlov's handwritten slides in djvu from a 5-lecture course in Bonn

• djvu, but the link is temporary

For derived categories per se, apart from Gelfand-Manin methods book and Weibel's hoological algebra remember that a really good expositor is Bernhard Keller. E.g. his text

• Bernhard Keller, Introduction to abelian and derived categories, pdf

...and also his Handbook of Algebra entry on derived categories: pdf

Kapustin-Orlov'a survey of derived categories of coherent sheaves is pretty good,

• A. N. Kapustin, D. O. Orlov, Lectures on mirror symmetry, derived categories, and D-branes, Uspehi Mat. Nauk 59 (2004), no. 5(359), 101--134; translation in Russian Math. Surveys 59 (2004), no. 5, 907--940, math.AG/0308173

but more slow/elementary exposition starting with fundamentals of derived categories is in an earlier survey of Orlov

• D. O. Orlov, Derived categories of coherent sheaves and equivalences between them, Uspekhi Mat. Nauk, 2003, Vol. 58, issue 3(351), pp. 89–172, Russian pdf, English transl. in Russian Mathematical Surveys (2003),58(3):511, doi link, pdf at Orlov's webpage (not on arXiv!)

There are also Orlov's handwritten slides in djvu from a 5-lecture course in Bonn

• djvu, but the link is temporary

For derived categories per se, apart from Gelfand-Manin methods book and Weibel's homological algebra remember that a really good expositor is Bernhard Keller. E.g. his text

• Bernhard Keller, Introduction to abelian and derived categories, pdf

...and also his Handbook of Algebra entry on derived categories: pdf