Guys, you're all recommending true complexity theory books -- Arora and Barak contains all sorts of things like PCP, Interactive Proofs, Quantum Computing and topics on Expander graphs -- things that most programmers/software developers have never heard of or will ever use. Papdimitriou is in the same category. Knuth is freaking impossible to read (and I was a CS/Math major) and gives zero intuition on how things work.
If you want a simple way to compute runtimes, and to get the flavour of the analysis, try the first chapter or so of Kleinberg and Tardos "Design and Analysis of Algorithms", that holds your hand through the fundamentals, and then you can work on much harder problems.