First - Organizing, Clean-up and Storage of general Legos. These are the Legos my boys share. Not specific sets that they keep separate. Here is how we keep them contained and do really quick clean up. Photos are of my son Christopher, he was playing and agreed to do the demonstrating for us.
So you start by having all the Legos you child plays with or wants to keep in together on a sheet. This sheet is a single bed sheet and fits a lot of Legos. When they play they should try to keep the Legos on the sheet. They will get better with that as they use the sheet and see its purpose and how easy it is to do the clean up.
Ds Christopher says if you do not have at least 8 parts of the sheet in your hand you will loose parts out the side while trying to pick it up... so
He pulled the middle of one of the sides out, shook it so that the Legos would go down into the bottom. Then he grabbed the center of the side and added it to the corners he was already holding.
When your child is ready to play again it is easy to grab the corners and the sides into a big bunch and pull the "sack" out of the tub. Make sure you have it all or you may dump the Legos. Pick a wide area, clear of other toys, books, etc.
Spread the sheet out so the Legos have room to spread out when your child is searching for that one piece of Lego he needs to finish his project without them going off the sheet.