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Matt_Simpson comments on Open Thread: April 2010, Part 2 - Less Wrong
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What, in particular, is the tool your are looking for?
A First Course in Bayesian Methods is ~$50 used, and covers what I take to be the basics. I'm currently using it in a grad class in Baysian statistics (with a companion text for computing in R) and have no complaints - well, other than that it's not an all encompassing text.
The first edition of Gelman's text is going for ~$35 used (~$50 for the second edtion) and has the added advantage of actually being in UM's library (both editions). I've not read either edition, but I hear it's the general Bayesian text to get.
Thanks for the recommendations!
I am being intentionally vague about the nature of the task I need to perform, but it is not esoteric. I would expect the problem to be discussed in any good textbook and many undergraduate statistics courses.
Edit: I think I see the chapter in the table of contents of Gelman from Amazon's preview.