An easy way to keep puzzle pieces together is to put them in a plastic or mesh bag you can seal.
You can get small plastic or mesh bags that are made for craft supplies that are perfect for puzzles.
This type of puzzle organizer works well for puzzles if your child is older.
Puzzles with more than 48 pieces usually don't have a backing board. So you can't slide them into a puzzle rack. This means puzzle racks can't be used for standard puzzles which just have the pieces.
If you decide to use a bag to organize your child's puzzles remember to cut out the puzzle picture and pop it into the bag too. This will not only show your child which puzzle is in the bag, the picture will help show them how the puzzle needs to be put together. (It's hard to do a puzzle when you don't know what the finished puzzle should look like.)
You can buy bags like the two shown in different sizes at Amazon. It's a good idea to buy bags in different sizes to suit different sized puzzles. It's also best to buy clear bags so you can see what puzzle is inside without having to open the bag.
Picture: In the Galaxy 60 Piece Puzzle (available at Amazon).