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Advice

"No one wants advice - only corroboration" - John Steinbeck

Following are the two most important lessons that I have learned for doing great research:

Every morning, write at least five pages in a research journal. (You can do this in 1-2 hours if you write stream-of-conciousness)
Periodically evaluate your progress as objectively as possible.
- Set two research goals for every day, week, and month and check at the end of every day, week and month whether you have met these goals.
- Ask the following questions periodically as you do research(thanks to Alan Schoenfeld):
  - What exactly am I doing? (Can you describe it precisely?)
  - Why am I doing it? (How does it fit into my plan for solving the problem?)
  - Am I making progress using this technique? (If not, can I come up with a new plan for solving the problem?)

Principles of Effective Research by Michael Nelson (I've found this paper to be very useful)
How to Write Your Dissertation in 15 Minutes a Day by Joan Bolker (Henry Holt and Company Publishers) is a great book for learning the process of doing research.
Getting What You Came For by Robert Peters is a very comprehensive book on how to plan your career as a graduate student.
Getting Things Done by David Allen gives good (and non-obvious) time-management advice.
How to Solve It by George Polya is a great overview of how to solve mathematical problems. The ideas in the book are very useful for doing research in theory.
Alan Schoenfeld, a mathematician at Berkeley, has done some fascinating research on how to improve mathematical problem solving abilities. There are some great, empirically proven, ideas in the paper "Learning to Think Mathematically: Problem-solving, Metacognition, and Sense-Making in Mathematics" which is available here. Note especially the figures and discussion on pages 61-70 of this paper.
(This paper also appears as Chapter 15 in the book "Handbook for Research on Mathematics Teaching and Learning" (D. Grows, Ed.).)
Collected Advice on Research and Writing
How to Present a Paper in Theoretical Computer Science
How to write an abstract
Computer Science Reading List In particular, see the section on articles and papers.

Impress your professors by: 1) doing really well in a class, 2) doing well as a TA for a class, and/or 3) doing good work on a research project the professor is working on.
A good letter of reference from a well-known professor is an extremely useful tool for getting a good job or getting into a good graduate school.
Check out the Career Center web page for advice on how to start building your career. It's never too early to start thinking about this.