The cell membrane is responsible for a lot of movement and actions of the cell. One of those actions is osmosis, which is the movement of water across a cell membrane. By allowing liquids and small atoms, such as oxygen and water molecules to pass through, this equalizes the concentration of that matter on both sides, so that the concentration is equal. This process is called diffusion. When this process works correctly, this is called isotonic as both sides have equal concentrations, but when this doesn't occur you are left with hypotonic and hypertonic concentrations. Hypotonic is the side with a lower concentration, and hypertonic is the side with a higher concentration.
Facilitated diffusion, which is the third kind of active transport, is very selective, and only allows one kind of particle through. Like the golgi apparatus, it transports things, and to do that facilitated diffusion uses carrier proteins. Like osmosis, facilitated diffusion moves those molecules from areas of high concentration to areas of low concentration, with a concentration gradient, and facilitated diffusion also uses no energy, as it's passive transport. The way that the molecules get through are either particles fit into one side of the protein then change shape and then get released, or they use gates in which one molecule bonds to a carrier protein then the gate opens, and the molecule passes through.
Carrier mediated transport is dependant upon specific carrier proteins and other types of molecules to move around important parts of the cell. Unlike passive transport, the carriers exist in multiple forms, such as proteins. Unlike passive transport, some carrier mediated transport requires energy to function. In the case of carrier mediated transport the carrier can sometimes be the membrane, or whatever substance is guiding or transporting the molecule or substance.
Endocytosis is a process which plasma membrane engulfs and takes substances into the cell, and is made up of multiple parts. First there phagocytosis which is a Pac-Man like shape along the cell membrane which engulfs food particles to be used in the cell, and or thrown out as a waste product. Then, the membrane forms a sac or vesicle which breaks off into the interior of the cell. Thoses Pac-Man like shapes have a specific name, and are called amoeba. Also, endocytosis uses molecule binding receptors which form inward vesicles, that are used to transport cholesterol. Then you have pinocytosis in which the amoeba take in liquid droplets by engulfing them.
Although exocytosis appears to seem like it's similar to endocytosis, it's actually the reverse of it. It's used for expelling waste and secreting substances from the cell, like a garbage truck. Vesicles that fuse with the membrane move to the plasma membrane then rupture open, and expel the unnecessary substance.
Active transport, like exocytosis often involves the cell membrane. Active transport, which uses energy, expels and brings in substances from in and out of the cell, and moves from an area of low concentration to an area of high concentration, against the concentration gradient. Because active transport uses energy, it uses techniques that use proteins and pumps to move around the substances within the cell.