A great collection of advice and links on the subject is here. For the (prospective) graduate students in mathematics, Terence Tao provides excellent advice here, and there is a whole new blog on the subject. As for the physics students, go here and here. See also my earlier posts, especially here and here. Some interesting material can be also found here and here.

*Update* (via ZapperZ blog): More advice from the Science Careers: here, here, and here.

*Update 2*: excellent advice for the graduate students in math is available at the Secret Blogging Seminar, here and here.

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