This is one of the best explanation I have read:

An Intuitive Explanation of Bayes' Theorem http://www.yudkowsky.net/rational/bayes

and I see Eliezer now recommends this instead: https://arbital.com/p/bayes_rule/?l=1zq

In the orbital link I selected deep math knowledge to see the subject form various angles. Immediately I read this on the page "This means that the odds over H will be proportional to the probabilities over H", that is completely wrong and misleading. Sorry to be hash.

I came into the comments to ask if anyone could remember a guide that was popularly recommended on HN in the past and it was your first link, so thanks for those :)

so i've never met the chap who does this blog (i think his name is Will), but i've been reading it for a while now. Don't let the post with pics of legos mislead you--this guy knows what he's talking about. In particular, his posts on parameter estimation and MC simulations are excellent. His writing style is unpretentious and patient (ie, not "see how smart i am" but "here's this fascinating subject that i really want you to understand") and in every post i've read on this Blog, he's got something interesting to say even for those who work in this discipline.

His name's Will Kurt - if you want to hear him talk a bit about his blog, he was the first guest on the Becoming a Data Scientist podcast: http://www.becomingadatascientist.com/2015/12/21/becoming-a-...

His blog is great, as you say: even if you know the topic you'll find something new there.

There's also Think Bayes (http://greenteapress.com/wp/think-bayes/) which uses python.