Almost all dies from any company can be used on the Sizzix Big Kick. Size is the only real limitation as you cannot cut anything wider than the machine. Longer platforms for longer dies are available.
A sandwich is the basis for using all die cut machines. It requires a solid base, usually about 1/2 inch thick. On this you would place one of two transparent "cutting plates." (These are relatively inexpensive and will need to be replaced over time.) Next is the die with the cutting edge up and, on top of it, place the cardstock or paper to be cut. Be sure the printed side of the paper faces the die. Now, for the top of the sandwich, place the second transparent cutting plate. You are ready to crank the handle and be amazed. Just think of the two cutting plates as the bread with the die and paper as the meat and cheese.
I have tried different die cut machines and love my Sizzix. It is the machine least likely to need shims (additional layers of paper) to cut evenly. No machine is perfect, however, and you will achieve best results if you place dies and paper toward the edges of the sandwich. Just be careful that nothing sticks out past the cutting plates.