To get started on this check out this paper:
That's a good survey article on the Langland's program. It's takes you through the historical perspective to Artin reciprocity and it's implications. If you look that over you'll get a good overview of what you need to know; class-field theory, L-functions, p-adic numbers, adeles, automorphic forms, and group representations. To get a good handle on this stuff check out Frohlich and Taylor:
I have a copy of this book and in my opinion it is accessible to someone with a good course in Number Theory and perhaps two courses in Algebra at the grad level. I don't think an undergrad is going to get there on his own but with guidance from an advisor working in number theory you can do it.
Now I'm no expert in Langlands but (I believe) the Langland's program is a series of conjectures that are basically consequences and generalizations of Artin reciprocity.
Give it a shot. The Langlands program is some deep stuff that took on a role of the same magnitude as Klein's Erlanger program before it. You really can't go wrong getting to the bottom of this one.