Honestly after a few days it just becomes second nature. We have a bin under the sink with biodegradable bags for the compost stuff (which we take out to the green bin every few days), a large recycle bin in the walk in pantry that we typically have to empty into the big blue bin once to twice a week, and a regular garbage bin which hardly gets any use.
So instead of cleaning plates off into the garbage, we clean them off into the compost bag. I rinse pudding containers or sauce containers right away after they're empty and throw them into the recycle.
Cleaning up after one's self gets done anyway, sorting while doing it doesn't add any effort. The only real extra effort is cleaning off things that are going into the recycling that had food in them. Worst case I throw those into the dishwasher with the dishes lol.