I was recently introduced to dimensional analysis and I wanted good references for learning the ideas behind it and representation of the natural world. I'm a grad student in biology. I don't have much of a physics background.
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This is a great summary of dimensional analysis written by Ain Sonin, a former professor of mechanical engineering at MIT. It's only ~50 pages, and most of it should be accessible to you. Though some examples may draw on parts of physics you're not familiar with, it is very well-written and should clarify the subject greatly.
A very good book, with more than 200 worked-out examples, is 'Applied Dimensional Analysis and Modeling' by Thomas Szirtes, MacGraw Hill, ISBN 0-07-062811-4