Each issue essentially covers a standalone adventure for the Doctor. In each period, the Doctor and his companions go through an adventure and towards the end the companions are made to disappear somehow. As the overall series progresses, we get more and more glimpses of the man behind the kidnappings and the Doctor also gets more and more insight into who is attacking his various incarnations in this manner. Given it's a 12-issue series, you know things will end with a big confrontation between the Doctor and this hooded figure in one rather epic conclusion to things.
The quality of the writing is pretty good all-throughout. As much as the Doctor is supposed to be one character with many faces, we have to admit that he takes on rather unique personalities withe very regeneration. And thus to write stories for each of those Doctors means being able to highlight how each Doctor is different but at the same time still show that he's he same man. That's not an easy task for anyone. But the Tiptons manage to get this done.
The villain in this story was a very nice reveal, I have to admit. Hooray for the Tipton's clever use of an existing TV character to really bring this story together. The motivations of our villain are pretty understandable given past circumstances and thus the adventure doesn't feel too cheap. Sure, it doesn't exactly end with one of the best endings for any comic book, but it still makes for quite the enjoyable comic book adventure.
If you ever want to get into the recent Doctor Who comics, then Prisoners of Time is a nice entry point for you to get acquainted with how the Doctor works in this medium.