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](https://arxiv.org/abs/math/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](http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=629&volume=58&year=2003&issue=3&fpage=89&what=fullt&option_lang=eng), English transl. in Russian Mathematical Surveys (2003),58(3):511, [doi link](http://dx.doi.org/10.1070/RM2003v058n03ABEH000629), [pdf](http://www.mi.ras.ru/~orlov/papers/Uspekhi2003.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](http://www.irb.hr/korisnici/zskoda/orlovMPIslides.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](http://www.math.jussieu.fr/~keller/publ/cam.pdf) 

...and also his Handbook of Algebra entry on derived categories: 
[pdf](http://www.math.jussieu.fr/~keller/publ/dcu.pdf)