Enzyme inhibitors come in two flavors: reversible and irreversible. Irreversible inhibitors act by forming a covalent bond with the enzyme. (Covalent bonds are very strong and difficult to break.) Aspirin and penicillin are examples of irreversible inhibitors. Aspirin modifies the Serine516 residue of the enzyme cyclooxygenase, by adding a COCH3 (acetyl) group. The residue is part of the enzyme's active site, and the acetylation causes it to lose its function.
Reversible inhibitors also have three types: competitive, noncompetitive, and uncompetitive. While the names of the second two are rather confusing, a competitive reversible inhibitor is straightforward: it mimics the structure of the substrate of the enzyme. The enzyme's active site thus bonds to the inhibitor rather than the substrate.
An uncompetitive inhibitor binds only to the enzyme after it has already bonded to the substrate. It might perform by blocking the release of the product from the enzyme.
A noncompetitive inhibitor binds to the enzyme at a point other than the active site, causing some reaction, possibly a change in the conformation of the enzyme, that interferes with the working of the enzyme. It may bind to the enzyme itself, or it may bind to the enzyme/substrate combination.