I put them in small plastic dishes labelled Port and Starboard. The dishes were from a lady handing out samples of something edible at Tesco's - I told her I could use the dishes and she gave me about 50 of them! For larger parts, old margarine tubs are good.
For parts that I’ll be fitting straight away, I simply tend to put the ones for the right side on the right and those for the left side, on the left on my workbench. For ones that I may have around for a while, like assembled track runs for a tank, I usually put them on the corresponding sides of the open box that the model also sits in (next to my workbench) between working on it.