Anyway. As I said earlier glycolysis occurs in both aneorobic and aerobic respiration.  I should probably clarify that with aneorobic respiration there is no available oxygen, with aerobic respiration there is. So as we all now know, the products of glycolysis are: 2 pyruvate molecules, 4 ATP (for a net gain of 2), and 2NADH molecules. 

In aerobic respiration the two pyruvate molecules and the NADH will proceed to the link reaction, then Krebs cycle, and finally the electron transport chain. I did warn you it was a complex process... 

In aerobic respiration there will (in an ideal world- which isn't often the case) be a net production of 36 ATP molecules. 38 if you don't subtract the two ATPs needed to start the process during glycolysis. 

However, in anaerobic respiration only 2 ATP molecules total will be produced. Nonetheless, the pyruvate molecules will be further modified, for no additional ATP. Don't ask me why. I'm sure there's a valid reason... Anyway, if you happen to be a yeast cell, which would be interesting to say the least, you will convert the 3 carbon pyruvate into ethanol. Since ethanol is a 2 carbon compound, we know that pyruvate was decarboxylated to create ethanol. All in all you produce ethanol and CO2, because of the decarboxylation. I kind of like that word.

If, by the off chance that you are not a yeast cell, but an animal of some sort, you will convert pyruvate into lactic acid (also known as lactate). This is also a 3 carbon compound, so no carbon dioxide is produced. This tends to happen if you have insufficient oxygen during a period of intense exercise. This process also occurs in the cytoplasm, and also results in a net gain of two ATP. 

Hehem. Part 2, of the very long, and laborious process of cellular respiration. Also, might I add that the process I am describing is a simplified one. There's actually even more to this than I'm explaining... So yeah. Next step, the link reaction. 

Alrighty then. Let us begin. Glycolysis occurs in the cytoplasm of your cells. Not the mitochondria. Cytoplasm. Glycolysis occurs in all organisms, whether or not they undergo aerobic or anaerobic respiration, so that's cool.

It starts off with glucose, which is a 6 carbon molecule.
Glucose is then phosphorylated by two ATP molecules, making fructose 1,6 bisphosphate (still a 6 carbon molecule). 
This is a highly unstable molecule and thus splits into two 3 carbon molecules called glyceraldehyde-3-phosphate (G3P for short).
This splitting process is called lysis.
Once all this has occurred there is an even more wordier and lengthier process whereby the two G3P molecules are oxidized, involving ATP synthesis and the reduction of NAD+ (coenzyme).
Both of the G3P molecules are oxidized forming a NADH (reduced NAD+).
The released energy of the forming of this coenzyme is used to add another phosphate to each of the G3P molecules.
Leaving us with a G3P molecule with two attached phosphates each.
Our busy friends, the enzymes, now remove all four of the phosphate groups and add them to four ADP molecules, to form ATP.
We are now left with pyruvate, whoopee.

This is only the beginning... Brace yourselves, it's going to get more complicated.