In order for something to become a new species, there has to be a big enough genetic difference that occurs that makes mating with each other unsuccessful impossible. When a new species is formed, it is called speciation. When I was looking up the different way speciation can occur, I found four modes that seemed the most important that I will list below.
Allopatric: new species formed from geographically isolated populations
Peripatric: new species formed from a small population isolated at the edge of a larger population
Parapatric: new species formed from a continuously distributed population
Sympatric: new species formed from within the range of an ancestral population
(Link: https://evolution.berkeley.edu/modes-of-speciation/)
If you are still a little confused, I found this chart to be helpful! In fact, the picture comes from a set of slides created by a professor(?) at the University of Washington. It is chalked full of examples of all these modes as well as a more in depth analysis of what they are!
(Link: http://courses.washington.edu/gs453/lectures/lec23.pdf)
(Edit: it seems like this picture is not loading. It is located on slide 14 on the powerpoint. My bad!)
After reading a bit more into these modes of transportation, I definitely think the speeds of which they happen are all different. As for the fastest mode, I think it would have to be allopatric speciation. This seems to be the mode that happens the most naturally, so therefore it's probably naturally selected. Plus, this only occurs when there is a physical barrier. It seems that once a barrier is put in place, things quickly evolve to be different. Additionally, when a population is split up, it reduces the population size. This means that mutation has a much bigger effect, and can gain a foothold quicker in the population, or that's what I think at least!)