I visited a men's specialty shop that had a massive glass brandy snifter on a table. It must have been 18" tall and 12 inches wide. The owner would just grab a pocket square, put it into a loose ball and toss it into the glass container. It was a very colorful display. When he selected a shirt and tie, he would just look at the container and reach in a pull out whatever color seemed to work. It was actually fun to watch and it was so much more effortless than folding, hanging, etc.
I have a small vintage mahogany tray. I fold then and fan them out. The seasonal ones I put away with my other seasonal clothing in hanging canvas garment bags that are stored in a separate bedroom. That reminds me, it is about time to pull out the spring and summer pocket squares and put away the fall/winter ones....
I bought a clear plastic jar from Wal-Mart to put my pocket squares in. Works for me!