what two substances control the movement of materials into and out of the cell?

I'd have to say water (controls concentration gradients) and proteins (which form channels for things that can't cross the membrane by themselves).

The membrane itself and the channels through it control most of it. There's a lot more than just two substances involved, however. There is the concentration gradient across the cell membrane; there are internal pumps the cell uses to move things OUT of the cell, and membrane "pumps" that pull things into the cell; there are lots of other things involved.

It's really interesting, and a fascinating bit of engineering altogether; the more I learn about it, the more interesting it gets.

It could be the Cell Membrane and Cell Wall if in plants.

Osmosis and diffusion