Labels are your friends
What we do in our shop is keep the KOP Totes and put different parts in each one. IE Motors, PVC, Wheels etc. For screws, bolts, nuts and other smaller such objects, we plan to use little pull out shelves which will be better for organization (right now they're in boxes in totes)
For tools, we use these:
http://www.milcompass.com/toolbox/3_7bx3mx9tbg.jpg. We have one set for mechanical tools and another for electrical tools.
For electrical and mechancial we also have two cabinets where we put our other stuff that doesn't have a place anywhere like paint, grease, new orders, extra medals etc.
At competition we usually bring things in totes or if the comp is local (like SVR) we load everything into a truck (the tool chests, cabinets, and some totes) and ship it off to comp on thursday.
Hope that helped!