So, I read the book some weeks ago. In the books, it is not explained, but we can assume based on the two cases we are presented. Miss Lucy's successful transformation and Mina's failed one. Here is how it goes:
First Dracula encounters his victims, these encounters being at night, IIRC at the hour of the wolf. In these encounters, the victims get hypnotized, it was easier when done with Miss Lucy, since she has somnambulism. Dracula drinks the blood of his victims from the neck, where after the events two small holes can be seen, resembling a wider rodent bite. Now the transformation has begun, and on the next day the victim wakes up pale, extremely tired, and ill looking.
Here the events are different for our two victims.
In Miss Lucy's case, her friends are late at finding out that Dracula is feeding on her, he continues to do that for several nights. Each time, Miss Lucy is paler, weaker and more exhausted. Towards the end of the transformation at night she begins to look healthier and better looking, her teeth a bit sharper. And then... she simply dies! Just after death she fully transforms into a vampire. When the friends enter her crypt during the day, Miss Lucy can be seen as a dead corpse. But at night she is a terrible vampire who can transform into a gaseous form and inspire lust in men.
With Mina Harker, the friends have noticed the attacks at much sooner. Dracula is unable to feed on blood nightly (like occurred with Lucy), the transformation continues nonetheless, but at much slower pace. The signs are the same, Mina begins to get weaker and weaker. At one point, she begins to look more vampiric. At that time, they notice that the minds and thoughts of Mina and Dracula are linked at specific hours: Sunrise and Sunset (Van Helsing begins to use that link to hypnotize Mina and gain information about Dracula's plans). Mina never fully turns into a vampire; when Dracula is killed, Mina's transformation stops. This seems to demonstrate that the transformation is not fully biological, but partially mystical.
Edit: During one hypnotic session, Mina tells Van Helsing she is not able to resist, and drinking blood from Dracula's chest. We're not told if the same happened with Lucy.
If I am not mistaken, Lucy's transformation occurs between 1 and 2 weeks. Mina's transformation must have taken about 4 and 8 weeks. (Not with the book right here).
So, what I can presume from the two cases we're presented:
- The transformation is slow, and depends directly on the encounters between victim and vampire. In theses encounters the victim is not in control of her body. Vampire feeds on victim's blood.
- In the early stages, the victim gets sick, extremely tired and pale.
- In the final stages, the victim's varies between the states of "almost dead" during the day and "almost vampire" during the night. Here the victim has a link to the master vampire's mind. The links are stronger at sunrise and sunset.
- Only after death does the victim's turns into a vampire. As seen with Lucy, the victim is a dead corpse during the day, and a vampire at night.
- If the master vampire is destroyed the process halts. The victim reverts to healthy living state.