How much control does the Doctor have over the TARDIS? In countless episodes it is portrayed as having a mind of its own, and not always doing exactly what the Doctor wants it to do.
It varies. Wildly.
- The Doctor took a course on how to pilot a TARDIS. He failed.
- The instruction manual for the TARDIS was flung into a supernova.
- The TARDIS seats six drivers. The Doctor works all six stations himself.
- The TARDIS does have a mind of its own, which when introduced empatically states that it takes the Doctor where he needs to go rather than where he wants.
Although the Doctor is extremely clever and manages to mostly pilot the TARDIS by himself, there's so much error range introduced by all of the above factors that his landing accuracy is always vague.
Or possibly more accurate, the Doctor pilots badly enough that the TARDIS finds plenty of ways to sneak in its influence to get where she feels he needs to be.
It varies. Sometimes he demonstrates pinpoint control: for example in "Kill The Moon", the Twelfth Doctor is able to materialize at the very second Clara switches off the countdown. Other times, he's not even able to get the right planet or century; for example, for much of the Fifth Doctor's tenure he was unsuccessfully trying to return Tegan to 20th century London, but failing completely.
I think the TARDIS can choose where to go if she wants, but she does let the Doctor pilot her. There was one time where, when she was human for a little bit, said that she brought him "Wherever he needed to go" or something like that, so probably both of them can pilot her... this is weird-sounding for some reason. Pilot yourself? ;)