It's a chore, and they don't really organize well.
The best that I've found is to keep the related pieces in their own groups. That cuts down on the mess.
Mostly, though, I setup a large board, then leave it together for later use. That is, one or more pieces of foam core with tiles affixed with poster tack.
For assembly, what ends up happening is a sprawl of tiles across my living room floor. Finding the right piece for an assembly can be a challenge, with the limited distribution of the different tiles.
For storage, I use appropriately sized plastic containers from Office Depot. They have a wide variety of sizes, several of which work well for the tiles. Not much organization there, but at least a way to keep them together and safe.
Thx!
TomB