You should be able to draw this graph and know what happens to the Km and Vmax when either a competitive inhibitor or a noncompetitive inhibitor is added to an enzyme solution.

When a drug is a competitive inhibitor, the drug competes with the normal substrate for the active site and the concentration of competitive inhibitor must be kept high at all times.  If the concentration of the competitive inhibitor drops, the velocity of the reaction will increase.

When a drug is a noncompetitive inhibitor, the drug binds strongly to the enzyme and does not compete with substrate.  Only the initial concentration of the drug is important since once the drug binds to the enzyme, it is not released.  The reaction rate of the enzyme will not increase as the concentration of drug (noncompetitive inhibitor) drops.  So, with a noncompetitive drug, you only have to administer the drug once or twice a day.  If the drug binds strongly enough, the rate of the reaction will only increase as new enzyme is synthesized.

Graph of competetive and noncompetitive inhibition.