It depends! Just how big is this case? They do come in several sizes. A typical ATX tower case is around 19 inches deep by 17 inches high by 8 inches wide. You can get larger and smaller ones.
Twice the size of the motherboard - yes, that's not wrong. You need space for the CDROM and hard drives, floppy drive (if you still use one), power supply, etc. Those really shouldn't overlap the motherboard, or it makes it hard to get to stuff.
Removing the innards and fitting them into a new case isn't difficult, but it's more complicated than fitting a graphics card. There are lots of connectors that go to places all over the motherboard, and you have to get them to the right places (and in some cases the right way round, and onto the right pins where there are more than your plug has). The new case will have new leads, which may be in different colours.
They do normally have nice, easy labels on them - so if you note carefully what was on each label as you remove it, and which way round it was (flat/printed side, or not flat/not printed) you should be able to have fun.
Don't forget to remove the power lead, and to use an earthing strap from your to the case before you start. Static built up from a carpet will soon destroy the chips in a PC.