Passive Transport: When molecules move across the plasma membrane from an area of higher concentration to lower concentration, requiring no energy from the cell.

Osmosis is the diffusion of water molecules, meaning that the water molecules are moving from an area of higher concentration to lower
concentration. No energy is required.

Isotonic: the concentration of solute inside and outside the cell are equal
Hypertonic: the concentration of solute inside the cell is less than outside the cell; the cell shrinks
Hypotonic: the concentration of solute inside the cell is greater than outside the cell; the cell expands

To break it down, if there is a greater amount of water inside the cell, water molecules will want to go leave the cell
because there is a lower concentration outside, so the cell shrinks. If there is a greater amount of water outside the cell, water molecules
will enter the cell, where there is a lower concentration, causing the cell to expand.

http://www.vcharkarn.com/uploads/45/45796.jpg

Active Transport: When molecules move across the plasma membrane from an area of lower concentration to higher concentration,
requiring cells to use energy.
There are three main incidences when a cell will use active transport:
Exocytosis: Vesicles made by the cell fuse with the cell membrane, releasing their
contents into the external environment
Endocytosis: Plasma membrane surrounds the substance and pinches inward, creating an intracellular vesicle
Pinocytosis: Vesicle contains fluids (cell drinking)
Phagocytosis: vesicles contain large particles or cells (cell eating)
Here's an animation of active transport.

http://fajerpc.magnet.fsu.edu/Education/2010/Lectures/12_Membrane_Transport_files/image032.jpg

Need a visual of the plasma membrane? Need a better view of where molecules enter and exit? Check out the video!