You could read Jurafsky and Martin's Speech and Language Processing (2008 edition), which is the standard textbook in the field. It's long, and has a variety of topics, so I'd suggest reading just the chapters that really apply to your interests.
Further, the best way to learn is almost certainly to actually implement NLP algorithms from scratch. You could pick some standard tasks (language modeling, text classification, POS-tagging, NER, parsing) and implement various algorithms from the ground up (ngram models, HMMs, Naive Bayes, MaxEnt, CKY) to really understand what makes them work. It also shouldn't be too hard to find some free dataset to test your implementations on.
Finally, there are lots of tutorials out there for specific NLP algorithms that are excellent. For example, if you want to build an HMM, I suggest Jason Eisner's tutorial which also covers smoothing and unsupervised training with EM. If you want to implement Gibbs sampling for unsupervised Naive Bayes training, I suggest Philip Resnik's tutorial.