Let me reintroduce my answer by first off stating Doctor Who has no aurthorised canon. But let me also say that the Whoniverse does have an accepted base history establised ( fan canon if you will ) by the diffrent media ( television, novels, audio, comics ) it is in. It is a history that in some cases is heavily debated. The debates arise out of what one wants to "accept as canon". Where much of the debates arrise over is what certain Whovians want to believe. ( i.e. the two stories of Atlantis ) But it boils down to if it is in one of the affore mention venues it can be accepted as "loose canon" if one wants. After all it is make beleive.
The most accepted form of official history is the televised series and that is what most consider "canon" bacause many dont follow any other venue. This is why so much is tied into the t.v. show. Case and point Paul's Doctors audio adventure has been made official part of the televised series through "Night of The Doctor" .And almost so were the Panini comics. In 2007, Doctor Who: The Flood, strip editor Clayton Hickman says that Russell T Davies had authorised the comic strip to depict the regeneration of the Eighth Doctor into the Ninth Doctor at the end of the 2004–2005 arc. But was rejected.
With the following established let me move onto the question. One possible way is looming.Looming is an asexual process of artificial genetic reproduction. But another is by test tube science. See the following link.
[DOC] Treatment for DOCTOR WHO : The Key to Time treatmentexaple_2_drwho.doc Though the Time Lords propagate their race by artificial fertilization and test tube gestation, ... the Doctor is getting; after all, the Doctor couldn't have built it without him. ... When the fleet of capsules is used for nothing but sample and intelligence
Also from Paul on it is accepted he is half human, as much as it is accepted that Time Lords are asxual. ( The Doctors Wife, The End Of Time ) A woman has actually played the Doctor in "Exile". But how Pauls Dr. is accepted is open to interpretation ( see the Beginners Guide to Doctor Who and BBC's websight ) Also one way it has been handled is sugesting Paul's Dr. adventures in three different forms (novels, audio, and comics) take place in three separate continuities. As in "Zagreus" and "The Gallifrey Chronicles ". But "Mary's Story" contradicteds this. At even one time it was wonderd when the series returned if Pauls Doctor would be treated like the other two movies with Cushing " Dr. Who and the Daleks" and "Daleks – Invasion Earth: 2150 A.D" but that was put to rest in "Human Nature "as this accepted the movie as a bridge between old and new. And in "Night of the Doctor" went as far to include Paul's compainions from the audio as part of
the T.V. history.
( NOTE AS I AM NOT A 10 REPUTATION I CAN NOT POST MY LINKS TO SUPPORT MY FINDINGS. PLEASE LOOK FOR THEM IN THE COMMENT SECTION SND WHEN, IF, I REACH 10I WILL POST IN ANSWER. )
Again though with a fantasy story like Who that has nothing set in stone it really boils down on what the individuals imagination wishes to accept. one is right and no one is wrong. This fall all this could change depending on the series and it is already rumored that Capaldi is a one season Who and the next is a woman.