I was at the Smithsonian space exhibit, and I am wondering how they freeze-dry space food.

Freeze-drying is a special way of drying stuff. First you freeze it very rapidly at low temperature. The idea is to turn all the water quickly into very tiny ice crystals. Then you pump all the air away and keep the food in a vacuum. Then water molecules leave the ice crystals as water vapor without ever forming liquid water.
Ordinary drying with heat changes most foods so that they never feel or taste the same again. Freeze-drying gives a very dry stuff that becomes just like the original food when the water is put back.

You'd might like to know that very tiny organisms like bacteria can be preserved for years by freeze-drying. Then they can be made to grow again just by adding water. However, this works only for tiny one-celled organisms. Part of the trick is freezing very quickly to keep ice crystals very small so they don’t damage membranes and structures inside the cells.