It's not an easy thing to do.
Other than in specimen where DNA is available, we have to work with what we have in terms of fossilized hard parts and ichnology. And what we have is a very small biased representation of what was living at any time in the past. The factors determining preservation are working against us, organic compounds need ideal conditions (very rare) for preservation, the fossil record favours the preservation of smaller organisms, cause of death is a factor (fast burial is good for preservation, almost everything else isn't), and then what happens after death (diagenesis, metamorphism, weathering), and whether the fossil is uplifted to the surface or shallow subsurface for the present time. The chances any marine organism is preserved is very very small, for terrestrial organisms it is even smaller. Simply put, the vast majority of organisms are not preserved.
Nevertheless, we do what we can in terms of classifying the fossil record and it's clear how evolution drives diversity based mostly on morphology. It is difficult at the genus and family level (many species are still argued or changed, especially at the genus level), but we have a fairly good grasp at how orders, classes, and phyla are connected by evolution. Yes, we are missing documentation of a great number of species, but that does not discredit the connections we have made, most importantly at higher ranks.
To answer your question: We use the gradual changes in characteristics in different organisms over time to give us a map of speciation. Due to the problems with the fossil record, it may be difficult in certain individual cases, but overall patterns of speciation are obvious and well documented.