The process itself is notoriously secretive, as far as I know, so there isn't that much information about it.
But what I can tell you is that they make each generation sort of as they need them. All the time in that process, there will be multiple designs proposed (even for the same pokemon), which might or might not make it; that's how Shellos and Gastrodon ended up skipping the generation they were created for, and why we have things like Eeveelutions introduced in four different generations, or cross-generation evolutions (Scizor, Mismagius, Megas) or pre-evolutions (the babies, mainly), and it also explains the mess the games end up into when they have to introduce things like incenses, rocks, location evolution or even new evolutionary stones to explain how pokemon couldn't evolve in past games. In essence, it's a bloody mess.
For example, we've yet to see how they'll implement the Alola-specific regional forms into subsequent games; at least all the pokemon so far weren't explicitly tied to a region, so you could work around that for the postgame; no such loophole with Alolan pokemon.
So, as far as I know, the design team is comprised of various artists (some are also illustrators for the TGC) and Sugimori as the design head; I imagine they have various meetings to get on the same page about the staples like starters and legends, and from then on, everybody sets out to make what the generation needs or to work and present their own designs, even designs leftover from other generations, as Shellos and Gastrodon prove (it also means that most pokemon's designs can date back to as late as Gen1 and for various reasons, were introduced later), or even inside jokes, like Munna; I doubt they planned munna in gen1, but I do believe someone remembered that dialog and thought it'd be fun to actually make the pokemon (you can tell because Munna is particularly disjointed, design-wise, compared to most other pokemon; it's a psychic type with a pattern of pink flowers); all the designs pass by Sugimori, probably the director and team, and more meetings, where they suggest changes or approve them.
Of course, I imagine the mechanic aspects of each pokemon are also taken in consideration, but I believe it's likely they start with the design and go from there (smogon's existence, if nothing else, proves that pokemon are not usually made with much care into how weak or strong they are, mechanics-wise).
Basically, each new generation is a self-contained group that may (gen 2, 3, 4) or may not (5, 6, 7) relate to the previous ones in terms of connections between the pokemon in it; there's also no way to tell exactly when a pokemon was created, since all we can know is when it was ready enough to be added to a game, but basically, the process is that Sugimori and his team work on the pokemon they need, add new ones, maybe old ones that were never released, and rinse and repeat each new generation.
But again, this is mostly conjecture based on how design work usually is; there's very little we can know about how it happens, and most of what we do know is how it doesn't happen.
