The Cell Membrane

Before explaining how materials cross the membrane, the entire structure should be understood.
Picture
Click on image for link
Phospholipid Bilayer- In the image, a layer of phospholipids is pointed out, but also notice how there is another layer below it. As there are two layers, it is properly named the phospholipid bilayer. The polar heads are hydrophillic, meaning the heads have an affinity for water. The tails, on the other hand, are hydrophobic, meaning they repel water. These layers are the first defense for the cell.

Carbohydrate- Carbohydrates help form an outer covering that protects the cell. They are relatively unimportant on the discussion of transport

Transport Proteins- The most important part of the membrane (arguably), these proteins float in the membrane and transport very small molecules into or out of the cell.

The All Important Transport Proteins 

Picture
Click on image for link
There are two types of transport proteins, both of which use a different form of diffusion. Diffusion, as a reminder, is when a small molecule passes through a membrane. 

Picture A shows a pore, which is a from of passive transport. Passive transport means any small molecule can pass through an open aqueous opening. Picture B shows carrier proteins, which is involved in active transport. Active transport uses energy, while passive does not. Remember that transport proteins are only used to transport small molecules and ions. Water does not have to use the transport proteins, as will be discussed in the next section. 

Osmosis and Regulation

Osmosis is the diffusion of water across a semi-permeable membrane. This membrane is permeable to water, but not to other dissolved particles surrounding the cell. In order for osmosis to occur, the solution must either have a higher concentration of solute outside the cell (a hypertonic solution), in which case water will flow into the cell, or a higher concentration of solute inside the cell (a hypotonic solution), in which case water will flow out of the cell. When the concentration of particles is equal both inside and outside the cell (a isotonic solution), there will be no osmosis. 

Movement of water into a cell can put pressure on the plasma membrane of a cell, which could cause some animal cells to burst. However, some organisms, primary unicellular, have organelles called contractile vacuoles that can pump excess water out of the cell. However, organisms with cell walls, like plants, don't burst due to the wall keeping from the membrane from bursting and keeps the plant upright.  
Relating this back to transport proteins, passive transport is used to take a molecule from a high concentration to a low concentration to restore homeostasis.  Active transport is used to take a molecule from a low concentration to a high concentration, which is abnormal and thus requires energy. 
Picture
click on image for link