You should gently remind him/her via email or in person that you need the letter by a certain date. In general, you can thank your letter writers in advance for the letters that they are writing and this should remind them. If your letter writers are unresponsive, start thinking about other people who could write you a letter. You can store up to ten letters on AMCAS and you do not need to use every one of them. Generally, you cannot have too many letters so get as many strong letters as you can.
Is there anything else about letters of recommendation that I should know?
If you have any other questions, you can go directly to AAMC and look at the letter of recommendation FAQs.