There are arguments against TDD, some valid and some not. It's quite possible that you've heard some of them before, and likely that you've repeated some of these yourself.
Of course, testing takes time. Writing unit tests takes time. Adhering to the red, green, refactor cycle of TDD does take time. But, how else do you check your work if not through tests?
Do you validate that the code you wrote works? How do you do this without tests? Do you manually run the application? How long does that take? Are there conditional scenarios that you need to account for within the application? Do you have to set up those scenarios while manually testing the application? Do you skip some and just trust that they work?
What about regression testing? What if you make a change a day, a week, or a month later? Do you have to manually regression-test the entire application? What if someone else makes a change? Do you trust that they were also as thorough in their testing, as I’m sure you are?
How much time would you save if your code were covered by a test suite that you could run at the click of a button?
By writing tests, you're effectively doubling the amount of code you're writing, right? Well, yes and no. Okay, in an extreme case, you might approach double the code. Again, in an extreme case.
In some instances, consulting companies have written unit tests into a contract with a line item and dollar amount attached. Inevitably, this allows the customer the chance to argue to have this line item removed, thus saving them money. This is absolutely the wrong approach. Testing will be done, period, whether manually by the developer running the application to validate her work, by a QA tester, or by an automated suite of tests. Testing is not a line item that can be negotiated or removed (yikes!).
You would never buy an automobile that didn’t pass quality control. Light bulbs must pass inspection. A client, customer, or company will never, ever, save money by foregoing testing. The question becomes, do you write the tests early, while the code is being authored, or manually, at a later date?
Testing can be difficult. This is especially true with an application that was not written with testability in mind. If you have static methods and implementations using concrete references scattered throughout your code, you will have difficulty adding tests at a later date.
I don't know how to test is really the only acceptable answer, assuming it is quickly followed by, but I'm willing to learn. We're developers. We're the experts in the room. We're paid to know the answers. It's scary to admit that we don't know something. It's even scarier to start something new. Rest assured, it will be OK. Once you get the hang of TDD, you’ll wonder how you managed before. You'll refer to those times as the dark ages, before the discovery of the wheel.