Here are some references (which are not mentioned in Resolutions of Lie algebrasResolutions of Lie algebras).
First I can recommend the book of Charles A. Weibel, An Introduction to Homological Algebra. It answers your questions and has a chapter where the general theory is made explicit for Lie algebras.
Secondly, the book of A. W. Knapp on Lie groups, Lie algebras and cohomology. This has many details and many examples.