David Tennant has done a lot of WHO work in the past, although not for the TV show. He was one of the actors in the audio dramas introduced during the show's "Wilderness" years. Tennant's performance is somewhat more traditional than the somewhat 'sad' Doctor Eccleston potrayed, although each Doctor is unique.
Doctor Who has never had a stable cast. Doctor actors usually stay for a few years and then depart (There have been ten so far). The longest running-and perhaps most popular-is Tom Baker, who inspired a lot of Tennant's performance. Sort of like the James Bond actors, in a sense. This has been going on since the mid '60s, and the companions/supporting actors leave at an even more rapid rate, although some last longer than Doctors do (Rose being one, and Sarah Jane was around longer than Colin Baker was)
How it works is something called regeneration, which is explained earlier in the thread.