How do I politely ask a teacher to write a reference letter as soon as possible? I have 3 days left and I totally forgot I could add more than 1 reference letter to my application.

I need this teacher to write me a reference letter as soon as he can... and it feels so rude asking this. 

How can I imply that subtly but clear enough for him to understand my situation?

Should I send him reference letters written by other professors to help him quickly find the form and content for the letter he will write?
Just go and talk to him.Tell him about how much you need the placement and how valuable his recommendation-letter would be to you (don't try to butter him/her).Be frank and kindly request him/her but be brief and direct. Don't worry teachers don't mind it,They want to help you as well.