The most useful size is 8'x4'and Bedlam normally owns several of these. They are held upright using braces, eyelets and stage weights. These can normally be found in the props cupboard, back stage right.
Flats need to be stored correctly or they warp over time and then putting them together is a faff. As most of the flats are warped the best way to assemble them is to lay them all flat and use a combination of either actors and G-clamps to hold them straight while you screw them together or use stage weight in place of actors. Stage weight tend to have slightly longer concentration spans.
Door flats are especially problematic. Firstly, if they get warped the sides won't be parallel and the door you put in it won't close properly forcing you to faff about. Secondly, they're much easier to warp because they're not squared off at the bottom which makes it much easier to accidentally twist them when storing them. The way to prevent this is to screw a piece of timber along the bottom. This will square it off and make if much less likely to warp. The same technique can be used to straighten a warped door on stage if its a stand along door flat. If it's not stand alone then you'd have to do the same to all the other flats or the door flat will be slightly higher than the others and that looks crap.
Flats are good for creating rooms or making the stage even smaller which can be very useful if you're trying to create an air of repression.