The process is explained in very good detail on the NATS recruitment pages.
http://natscareers.co.uk/indexfs.asp?id=200691
Assuming you want to be an ATCO then you will find that DerekTheElephant has it spot on. In addition, there is the online application form to begin with, and medical, security and "other enquiries" once you have successfully completed the selection process.
The careers pages are excellent, go do some reading.