(All of the below is IIRC.)

For a really basic introduction, there's Elementary Bayesian Statistics. It's not worth the listed price (it has little value as a reference text), but if you can find it in a university library, it may be what you need. It describes only the de Finetti coherence justification; on the practical side, the problems all have algebraic solutions (it's all conjugate priors, for those familiar with that jargon) so there's nothing on numerical or Monte Carlo computations.

Data Analysis: A Bayesian Approach is a slender and straighforward introduction to the Jaynesian approach. It describes only the Cox-Jaynes justification; on the practical side, it goes as far as computation of the log-posterior-density through a multivariate second-order Taylor approximation. It does not discuss Monte Carlo methods.

Bayesian Data Analysis, 2nd ed. is my go-to reference text. It starts at intermediate and works its way up to early post-graduate. It describes justifications only briefly, in the first chapter; its focus is much more on "how" than "why" (at least, for philosophical "why", not methodological or statistical "why"). It covers practical numerical and Monte Carlo computations up to at least journeyman level.

I second the question. "Elements of Statistical Learning" is Bayes-aware though not Bayesian, and quite good, but that's statistical learning which isn't the same thing at all.

I'm not intending to put this out as a satisfactory answer, but I found it with a quick search and would like to see what others think of it.

Introduction to Bayesian Statistics by William M. Bolstad

http://books.google.com/books?id=qod3Tm7d7rQC&dq=bayesian+statistics&source=gbs_navlinks_s

Good reviews on Amazon, and available from $46 + shipping... http://www.amazon.com/Introduction-Bayesian-Statistics-William-Bolstad/dp/0471270202