Simple diffusion: the molecule passes either through a channel or simply through the lipid bylayer. This is goverened by Fick's law for solutes:
$$Flux = \frac{K \cdot \Delta C \cdot SA}{\text{Thickness}}$$
Facilitated diffusion: the molecule binds to a protein, they move together through the lipid bilayer. Governed by Fick's law until saturated (e.g. aquaporins).
Primary active transport: The substance is moved, hydrolyzing ATP (e.g. the Na/K pump)
Secondary active transport: Substance one (usually sodium) is actively transported, then substance two is either symported or antiported with it. E.g. SGLT2 symporters, Na/Ca antiporters.
Exocytosis: Vesicle containing a substance to be secreted fuses with the cell membrane when activated by calcium, depositing the substance outside the cell.
Endocytosis: The cell membrane invaginates around the substance, absorbing the substance into the cell. A vesicle (or vacuole) may or may not be created. Endocytosis may be subdivided into phagocytosis and pinocytosis (big and small vesicles).