With TDD, you don't care much about design. The idea is that you must first learn what you need before you can start with a useful design. The tests make sure that you can easily and reliably change your application when the time comes that you need to decide on your design.
Without TDD, this happens: You make a design (which is probably too complex in some areas plus you forgot to take some important facts into account since you didn't knew about them). Then you start implementing the design. With time, you realize all the shortcomings of your design, so you change it. But changing the design doesn't change your program. Now, you try to change your code to fit the new design. Since the code wasn't written to be changed easily, this will eventually fail, leaving you with two designs (one broken and the other in an unknown state) and code which doesn't fit either.
To start with TDD, turn your requirements into test. To do this, ask "How would I know that this requirement is fulfilled?" When you can answer this question, write a test that implements the answer to this question. This gives you the API which your (to be written) code must adhere to. It's a very simple design but one that a) always works and b) which is flexible (because you can't test unflexible code).
Also starting with the test will turn you into your own customer. Since you try hard to make the test as simple as possible, you will create a simple API that makes the test work.
And over time, you'll learn enough about your problem domain to be able to make a real design. Since you have plenty of tests, you can then change your code to fit the design. Without terminally breaking anything on the way.
That's the theory :-) In practice, you will encounter a couple of problems but it works pretty well. Or rather, it works better than anything else I've encountered so far.