And this whole time I thought he built it! Well, I never watched Doctor Who so I have an excuse;)
In the movies, starring Peter Cushing as a human scientist named Doctor Who, he did in fact build it himself.
In the black and white episodes, it was mentioned that the Doctor stole the time machine but that does not seem to have been used lately. The BBC is afraid that kids will steal time machines.
I'm not sure it was blue when he stole it. It didn't get stuck in that shape until just before his adventures started on television.
He actually stole a tardis with a broken chameleon circuit, so it has been a blue phonebooth the entire time he has "owned" it. Except for one time in 1963 when he got it working temporarily. It did however select forms that did not fit into the environments it landed in. It broke shortly after. (First story of season 22)