Cell Movement

Diffusion is the process by which molecules spread from areas of high concentratiion, to areas of low concentration.
e.g: Oxygen molecules diffuse across cell membranes into cells, and carbon dioxide molecules diffuse out. Both compounds cross the phospholipid bilayer.

 Facilitated Diffusion-
Facilitated diffusion is when a molecule cannot just passively diffuse across a membrane; however, it requires a protein "carrier" and energy in the form of ATP to move across the membrane.
e.g: Glucose, sodium ions and choride ions are just a few examples of molecules and ions that must efficently get across the plasma membrane but to which the lipid bilayer of the membrane is virtually impermeable. Their transport must therefore be "facilitated" by proteins that span the membrane and provide an alternative route or bypass.

Active Transport-
Active transport is the movement of a substance against its concentration gradient (from low to high concentration). In all cells, this is usually concerned with accumulating high concentrations of molecules that the cell needs, such as ions, glucose, and amino acids. The process uses chemical energy, such as from ATP.
e.g: Sugar molecules go into a cell. It cannot pass right through like water and oxygen so it uses active transport.

Osmosis-
Osmosis is the movement of solvent molecules through a selectively permeable membrane into a region of higher solute concentration, aiming to equalize the solute concentrations on the two sides.
e.g: Osmosis occurs on your hands in the bath. When you're in the shower too long, your hands and fingers become wrinkly.

Endocytosis-

Endocytosis is a process by which cells absorb molecules (such as proteins) by engulfing them. It is used by all cells of the body because most substances important to them are large polar molecules that cannot pass through the hydrophobic plasma or cell membrane.
e.g: Leucocytes, neutrophils, and monocytes can engulf foreign substances like bacteria.