The Stanford NLP Group is always on the lookout for budding new computational linguists. Stanford has a great program at the cutting edge of modern computational linguistics. You should definitely apply!
The best way to get a sense of what goes on in the NLP Group is to look at our research blog, publications, and students' and faculty's homepages. Our research centers around using probabilistic and other machine learning methods over rich linguistic representations in a variety of languages. The group is small, but productive and scientifically focused.
Where do you apply for graduate (PhD or MS) study? Not directly to the NLP Group. Stanford graduate admissions are handled through individual departments, so you'll want to apply for admission through either the Linguistics Department or the Computer Science Department. Both departments have excellent graduate programs. Normally, you should apply to the one in which you have more background and greater interest in further study. Do make sure that you emphasize any research experience and results, and that you get letter writers who can speak convincingly about you. Decisions about admissions are made by the department's admissions committee. Because admissions committees represent the whole department and aim to select the best applicants regardless of specialization, you should direct your application towards an appropriately broad audience. And, as you probably know, Stanford admissions are quite competitive.
If you have questions about admissions, please check the graduate admissions web pages listed on the right, or write to the admissions email addresses listed. We NLP Group members attempt to answer specific NLP-related admissions questions (although sometimes we get too busy...), but in general it isn't necessary or helpful to contact us to let us know that you want to apply or have applied for admission.