How does a cell transport materials across the cell membrane?

Depednign on what the cell is trying to transport there could be a variety of ways for the cell to transfer materials.

If the item is small and np then it can go through the lipid bilayer.

Simple diffusion and facilitated diffusion are passive transport meaning the cell does not need energy to transfer the membrane

and active diffision means they need to spend energy.

you need transmembrane protiens to move things inside the cell