don’t be linear!

Work with the simplest special case which looks non-trivial.  Sometimes one can even work with a special case which is trivial by other methods, but which you cannot see to be trivial by the methods used in the paper.

Identify what is bugging you about a certain claim.  E.g. “How on earth can the author get from a statement of this type to a statement of another type?”, e.g. the author is deriving lots and lots of identities, but eventually will need some sort of estimate.  Then one should scan through the proof for the first point where an identity turns into an estimate; understanding this one step is likely to illuminate the structure of the entire argument.