Prepare for It. In this case, all you can do is politely deliver your resignation, then strive to make the transition as easy as possible for your team. Your manager may not have the ideal reaction to your news__and your workplace may not be the most pleasant environment for the next two weeks__but to avoid burning bridges, it's best to work through it with a positive attitude.
Why a Resignation Letter? In these digital times, why should we submit a resignation letter, anyway? A paper trail does seem old_fashioned, but in this case, it's a best practice. It makes your intentions clear, as well as the conditions. You're removing any ambiguity about the end of your time there.