I wrote a post on getting started with JAGS for Bayesian modelling. If you're keen to get started quickly then playing around with some variant of BUGS, such as JAGS, is a practical way to get started.
To quote the abstract of the post
This post provides links to various resources on getting started with
Bayesian modelling using JAGS and R. It discusses: (1) what is JAGS;
(2) why you might want to perform Bayesian modelling using JAGS; (3)
how to install JAGS; (4) where to find further information on JAGS;
(5) where to find examples of JAGS scripts in action; (6) where to ask
questions; and (7) some interesting psychological applications of
Bayesian modelling.
In particular, you may find it useful to study some of the example scripts mentioned in the post.