There are several different ways to aquire NLP skills while earning a degree depending on which department you choose to make your home. Here is a basic overview of the your choices.
CLEAR (The Center for Computational Language and Education Research)
As a student, much of your work outside of the classroom will be conducted within CLEAR, a center dedicated to advancing Natural Language Processing which houses many government funded research projects. The facilities include labs, meeting rooms, graduate student offices, and computing resources.
The Cognitive Science Combined PHD Program
The interdisciplinary Cognitive Science Combined PHD requires you to choose one department as your home and an additonal department as a second discipline.