Depending on how deep you want to go into it,
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has a good article on it.
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has a nice 20ish minutes video about it going over the math then implementation. Yes they are both about 3D but the principle is the same as 2D, you have an hierarchy of transformation matrices that you apply sequentially to transform the positional data related to the bone. In 3D case you transform vertices, in vector 2D you actually transform the origin points. Good thing is that you don't have to deal with the smoothingand influence that is needed for proper 3D model skinning.