I'm trying to learn class field theory and I'm wondering if anyone knows of any good sources with a bunch of examples on how to actually use it? This can be anything from books to course notes to course websites with solved homework. Interesting examples would be something like constructing specific extensions of $\mathbb{Q}$ and $\mathbb{Q}_p$, determining splittings of primes in more complicated extensions than the quadratics or anything else that is "concrete" where it might be useful.

My problems seems to be that while I can understand the actual statements it still seems like I can't see how to actually use it for any practical computations. By looking at the definitions it just seems like most objects aren't terribly computable. Most books just seem to have just some fairly trivial examples like e.g. finding the Hilbert Class Field of something like $\mathbb{Q}(\sqrt{-5})$ and the examples exists to just give an example of some defined object and do not actually use the theorems for anything.