Poke Pelago lifts from our shoulders the heavy burden that is the guilt of leaving Pokemon in the PC forever and provides them a fun outlet to play and give you, the trainer, goodies to benefit.
You'll unlock it as an option from the menu as soon as you've got Charizard Glide registered to your Ride Pager. This means you have to beat Kiawe's trial!
Mohn is the NPC who heads up Poke Pelago. Nobody knows where it is, but apparently your Charizard Glide can get you there, even if you're currently inside a dungeon or building. And once you leave Poke Pelago, you are put right back where you left from (includes inside a dungeon or building). Strange indeed.
Talking to Mohn via the sailboat icon in the bottom right of the touch screen will yield options by which you can manage the Pelago islands as a whole.
The first is Develop Isles. When you first open up Poke Pelago, you'll notice that it only consists of one island and the rest all need development. Furthermore, once the islands are developed, you'll need to develop them further to make everything the Pelago of your (and Mohn's) dreams.
These cost plain Poke Beans, so your spotted and rainbow beans are safe. You'll also need a certain minimum number of Pokemon in your PC. They don't have to be unique species, if you had 100 Pikipek you'd still be fine (but why would you have 100 Pikipek...?).
It's recommended you first develop Isle Abeens, so that you can get more Poke Beans to develop the remaining Isles faster. It also is the easiest to develop.
The second options lets you swap Poke Beans. Mohn will give you three plain Poke Beans for one Spotted Poke Bean, and seven plain Poke Beans for one Rainbow Poke Bean.
Considering that Spotted and Rainbow Beans, when fed to your Pokemon, give you more hearts to raise Affection faster, it might seem like a bad idea to give them all to Mohn. However, if you're trying to develop the Isles, you can only use plain beans! So trade them in and prioritize maxing out your Isles!
Finally, you can send a Bean Bottle. This is just for the social factor, and lets you send a handful of Poke Beans out into the Internet for other players to pick up. If you receive any Bean Bottles, they'll show up in Isle Abeens's shores and you can pick them up by tapping them.
If you're feeling particularly kind, send out tons of beans!