Write a short letter and next time you're at work see your manager. Tell him/her you have decided to leave and then hand them the letter of your resignation.
I've written you a short template for your letter below:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dear [insert HR or managers name],
I am writing to inform you that I have decided to leave my roles as [insert role]. I would like to thank the company for all the experience I have gained whilst working here.
Please accept this letter as my [number] days notice, as outlined in my employment contract. This means my employment will terminate on [insert date].
Warm regards,
[your name]
[your sigature]
[date of letter]
[contact details]
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Just give him/her the letter, say you are leaving. If they ask questions just say I'm going somewhere else - keep it brief.
If you're really nervous, try and give them your resignation letter the day before your days off before leaving your shift. This way you won't see them for a few days so they will be over it by the time of your next shift lol.
If possible, book a weeks holiday and hand in your notice before your holiday (still counts).
Hope I helped