Since I got an offer on the house I had listed for sale, I thought it was about time I finally got rid of all the paint that had accumulated in the shed. For reasons too long to go into here, I had A LOT of paint to get rid of. Not sure how they do it elsewhere, but where I am, the first Sat. of the month is hazardous waste day at the dump. I pulled up with an entire pickup truck load of paint - can after can after can.
While we were unloading I asked the guy what they do with it. First they empty out of each containter into a big vat. At the end of the day, after they are done piling up the garbage, and after they bulldoze it to pack it down, they spray the paint over the pile to “seal” it. That is about all the info the guy had. I guess by “sealing” he meant that it helps keep the loose bits from blowing around. My other guess is that this process gives the paint a chance to dry and therefore not leach directly into the soil/groundwater/whatever.
I’m sure the color of all the paint mixed together is some sort of turd brown shade, but I prefer to imagine a psychedelic rainbow fantasy out there. 
Here you turn in your paint and they save it all up to be mixed into various shades of brown (just as you suspected) and then given to our Graffitti Patrol to go paint over graffitti in town. We have many taggers, so the Graffitti Patrol is always busy. Of course, this means that several business have stripes of varying hues of brown paint on them.
In my community Latex paint is not considered hazardous waste. You add sand to it, let it dry out, and put it with the regular trash.
One of my summer jobs was painting schools with latex paint. At the end of the day we’d wash our brushes in a little janitorial closet, and get rid of the excess from the brushes by flinging it against the wall with the brush. This produces Jackson Pollock-like abstract paint squiggles. We called the closet “The Rainbow Room”. If we’d just mixed the colors together, it probably would’ve been brown, but this way it made a pleasingcomposition.
Until they tore the building down a couple of years ago.
Out here, they’re a smidge more sophisticated and they sort out and mix together the whites, the beiges, the browns, the grays, the greens and everything else gets stirred together into muck. This way, they can at least look like they tried to match the thing that got tagged, rather than globbing the same grubby brown onto everything.
Pretty similar to here - the wet, usable paint is gathered up for anti-grafitti uses, or some communities put it aside at re-use centers where people can pick it up for free, especially the mostly-full cans. The dribs and drabs go to the communal grafitti cover-up.
Dried paint’s not considered hazardous, and they say to just put empty/dried cans in the trash.