Unit testing, the testing of an individual piece of coded functionality by the team that wrote it, is a part of coding, not something different from it. Part of designing the code is designing how it will be tested. You should write down a test plan, even if it is only one sentence. Sometimes the test will be simple: 'Does the button look good?' Sometimes it will be complex: 'Did this matching algorithm return precisely the correct matches?'
Use assertion checking and test drivers whenever possible. This not only catches bugs early, but is very useful later on and lets you eliminate mysteries that you would otherwise have to worry about.
The Extreme Programming developers are writing extensively on unit testing effectively; I can do no better than to recommend their writings.