Stanford's NLP (Natural Language Processing = Computational Linguistics) course (taught by Chris Manning, one of the best known names in the field) is online, with both videos and transcripts available[1]. The standard intro textbook to the field is Jurafsky and Martin[2], which is an excellent read if you're at all interested in NLP/CompLing.
Having tried to teach myself this subject for the past few weeks, this was the best learning resource I came across. It explains things from the beginning with great clarity. Goes into formal grammars, the Chomsky Hierarchy, automata (finite state machines etc.), parsing, while providing enough grounding in set theory and graphs to get by.
A lot of compiler texts cover similar territory. The goals are different, but the basic tools and concepts overlap. (I particularly recommend Appel's _Modern Compiler Implementation in ML_.)
This comes through the interdisciplinary nature of computational linguistics: CS people know that theories and models are just theories and models, and can be mixed and matched to fit your application purpose better. (People love to have pillow fights over principles in programming language designs and other assorted stuff, but in the end you just choose something from the menu that looks tasty or cook your own using everyone's ideas).
Linguists, on the other hand, are after THE TRUTH (i.e., what actually happens in part of human language understanding), or a good model of it. It's not uncommon in linguistics that people will try and construct The One True Model and look down upon anyone who mixes and matches bits from multiple theories - because, anyways, only the grown-ups are supposed to create new ones, and everyone else is prone to mess it up beyond recognition.
Take together the blissfully ignorant mixing and matching habit from the CS side, and the linguistics habit of having mutually incompatible theories that fight over subscribers, and you get the seemingly incongruous habit of CL people to mix and match theories that are not meant to be mixed and matched.
I prefer "natural language processing" over "computational linguistics" because NLP/CL has very little to do with the goals of linguistics. Like you mentioned, linguists are after the truth of what actually happens in the mind to make language work. NLP folks are after what works -- any answer will do.
Being practical is fine, of course, but it just irks when NLP is billed as a science that is trying to "discover" something deep and real about the world. You often see young NLP students who take linguistics courses wanting to bring over some of the (cognitive) stuff they learned in these courses over to NLP. This is well-intentioned, but naive. NLP is an engineering discipline and, as such, the answer that provides the best results is the best one regardless of what it's cognitive viability is.
1: http://see.stanford.edu/see/lecturelist.aspx?coll=63480b48-8...
2: http://www.amazon.com/Speech-Language-Processing-Daniel-Jura...