where is the enzyme pepsin made (specifically), and where does the enzyme work?

its actually secreted from your stomach to help aid digestion;)

It is produced in the stomach and acts there.

It is produced by the chief cells in the mucosa of the stomach. It along with hydrochloric acid is the beginning of protein digestion.

The above answer is nearly right.

PEPSINOGEN is made in the chief cells (as they're called) of the mucosa of the stomach.  It is an inactive pro-enzyme.

Pepsinogen is secreted along with hydrochloric acid (HCl) in response to food.  When the two meet in the stomach, the HCl helps pepsinogen convert to PEPSIN - the active form.  The reason for initially secreting pepsinogen (inactive) is to avoid destroying the cell busy making it.

Pepsin is a protease, meaning it is capable of breaking down proteins.  It conducts its work in the stomach.  It is only capable of breaking certain types of bonds between amino acids, and so further digestion of the proteins is often required in the small intestine.