its not hard.
I have many jobs and all I do is get a resignation letter (btw there is a eb site to fill them out easily ) and put on it the time when you want to go...forget your contract for the minute.
Then when u give it to them, if they agree you go when you want. MOst people with real jobs need to give 4 weeks but I have never stayed longer than 3.
THey will talk to you about the date, if they think its a big deal just do whatever they say inline with your employment agreement, you dont want to upset them too much cos u never know when u may meet again.
Always thank them for the oppatunity and tell them the new job is helping you achieve your goals blah blah...try not t bag people out...or say to your boss she is a dumb bitch with no idea...haha I have the refrain every day.