I actually handed in my first 2 weeks about a month ago - I have worked before then but that one I walked out of on the spot, thats another story.
At the end of the day remember you dont owe your employer anything outside of the law - youre just selling your time to them and your notifying them you will no longer sell your time to them. Most will just go "oh okay wish you luck" and let you carry on with your job for 2 weeks. Sometimes they might just not schedule you after your employment date - and if youre contracted then make sure they pay you for that 2 weeks (most often its taken out of your holiday pay.)
Managers go through people handing in notices and leaving all the time, especially in most first jobs with a high turnover, so dont stress it too much. Just make sure you make note of any mistreatment just in case things start going wrong (which they probably wont) :)