The two forms of respiration are Anaerobic respiration and Aerobic respiration.

They both start the same way. It always begins with the initial breakdown of glucose. This is called Glycolysis. It's reaction is as follows:

C6H12O6 + 2ATP ------> 2Pyruvic acid + 4ATP

After glycolysis, this is where the difference starts. If there is no oxygen present, if the organism lives in an anoxic (no oxygen) environment, it will go into fermentation to continue to break down the organic molecules to produce ATP. There are two types of fermentation, lactic acid fermentation and alcoholic fermentation. The products of each are different. Lactic acid fermentation is used to make cheese and yogurt products, alcoholic fermentation is used to make alcohol products (beer, wine, liquor).