Writing Unit Tests for Existing Code?

out-of-order asks: "I recently became a member of a large software organization which has placed me in the role of preparing the Unit Test effort for a component of software. Problem is that everything that I've read about Unit Testing pertains to 'test-driven' design, writing test cases first, etc. What if the opposite situation is true? This organization was writing code before I walked in the door and now I need to test it. What methodology is there for writing test cases for code that already exists?"