What is the movement of materials through a cell membrane using the cell's energy?
The energy used is in the form of ATP (Adenosine Triphosphate) molecules.
The process is called Exocytosis when materials are transported out, and Endocytosis when transported into the cell.
Proteins are created in the Ribosomes and then by exocytosis they are put into vesicles that form around them and take them to the cell membrane. There the vesicles merge with the membrane and the proteins are transported to the outside of the membrane where a new vesicles is ready to transport the protein out.