Can some tell me how you can cut this stuff without it just falling apart.

There are different kinds of styrofoam. It depends on which type you have.
One is made up of many round, beads of foam compressed together. I suspect this is what you have. It is much harder to work with in many ways. You need a hot knife/wire for it and still there are problems.

I work with stryrofoam alot and I just use one of the stryrocutters from AC Moore or Michaels, They are only 20.00 and worth every penny. Basically it heats up and then you literally melt your way around the shape.It says to use genuine styrofoam products but I have used it on every kind without any probs.

Oh thank you all so much. I think i am off to the store.