There is an article in PSPUM-9, in Algebraic groups folder.
http://mathoverflow.net/questions/96542/tamagawa-number-of-elliptic-curves-over-mathbbq
http://mathoverflow.net/questions/95050/geometric-explanation-of-tamagawa-numbers
http://mathoverflow.net/questions/44184/why-are-tamagawa-numbers-equal-to-pic-sha
http://mathoverflow.net/questions/96542/tamagawa-number-of-elliptic-curves-over-mathbbq
nLab page on Tamagawa numbers