If you want to give a longer notice period, then give a longer notice period.
Nobody minds if you give a longer notice period - it helps them with transition planning - so I wouldn't worry about the "polite" aspect, as you're already being generous.
I'm unsure from your question if you're planning on staying until May 29th, or leaving at some time between now and then. If you're planning on staying until the end of contract, you don't technically have to give a notice period - the contract would just expire. However, letting them know a month early will not be taken poorly. If it is before then - even a day before - then yes, you should give notice.
You don't mention why you're leaving - I'm assuming here that you have another role lined up? Or maybe a holiday! All you do is just have a meeting with the manager, and then tell him/her that when the contract expires/on this date you'll be moving to a new role/partying on a beach.
They will appreciate the extended notice, which is useful if you ever need more work in the future.
The only reason you wouldn't give extra notice is if you think they'll turn around and give you 2 weeks notice. That seems pretty unlikely though.
