More precisely, I want to introduce and give examples of the things which occur when describing the local and global Langlands conjectures. So I will talk about smooth irreducible representations of p-adic groups, local and global Galois groups and their representations, and automorphic forms and representations. I will also say a little about the theory at infinity (so (g,K)-modules and so on).
I will spend a little time going through the classical definitions of modular forms, and then I will spend more time explaining how to construct the automorphic representation associated to a classical cuspidal modular form which is an eigenform for the Hecke operators.
If time permits I might even spend some time on the trace formula, and how it can be used to prove simple cases of Langlands' functoriality.
I also learnt a lot from the instructional programme run at the Newton Institute on this sort of thing, in early 1993. Scans of my notes (this time written in black ink) are here
I found the book "Algebraic number theory" by Cassels-Froehlich very helpful when I was learning stuff. Also, the conference proceedings commonly referred to as "Corvallis" (Proc Sympos Pure Math Volume 33, parts 1 and 2) was also very helpful; initially I used to look at Tate's article a lot, and I got older I started looking more carefully at the other articles.
I wrote a paper with Toby Gee called "The conjectural connections between automorphic representations and Galois representations". I suppose one could argue that the MSRI summer school is my attempt to teach the background necessary for reading that paper The paper is here.
Over the years I've written various notes on things like automorphic forms for GL(2) over Q, automorphic forms in general, Maass forms, principal series representations, representations of GL(2,R). I will probably use some of this material in my course.
The document which pushed me from the state of "not having a clue what the trace formula was" to "actually having some understanding of what the trace formula was", was David Whitehouse's wonderful notes. Thank you David.