Most algebraic number theory texts I've come across treat global and local fields somewhat separately. In practice, I know the technique is often to start with a question about global fields, and then take the completion at each prime $\mathfrak{p}$, prove the statement there, and use a local-to-global theorem to get back the statement over the global field.
I'm wondering if anyone has a good reference for the basics of what happens to number fields when you take the completion at a prime? I'm thinking of results like: if $L / K$ is an extension of (global) number fields, and $p \in \mathcal{O}_K$ lying under $q \in \mathcal{O}_L$, then $L_q / K_p$ is an extension of local fields with ramification degree equal to $e(q / p)$ and the like.
Ideally, there would be a survey/chapter etc. on the basic results about what happens when you take completions to go from global to local.
Edit: Adding the closest reference I've found: These notes from Drew Sutherland's MIT course are a pretty good approximation of what I'm looking for - Section 11.4 gives the main results, but I'm still interested in other options.