Ask early (1 month or more before deadline)
When you initially get in touch to request:
Remind them who you are (if you aren’t in regular contact) and why you think they would be an appropriate recommender. Remind them of the scope of their experience with you, and tell them why you are excited about the opportunity for which you are applying.
If they say ‘yes’:
Do everything you can to make the process as easy as possible for recommender.
1) Clearly tell them the date letter is due, and give them any link the need to submit electronically. Describe the opportunity for which you are applying, and why you are interested in it. Provide a paragraph description and ideally a link to the call for applications (note: do not send them to some general website they’d have to explore to find the information).
Remind them why you are awesome (attach CV and mention any specifics they could play up). Remember, you want to make it easy for them to write a killer letter.
If the submission must be via snail mail, provide them an addressed, stamped envelope to the proper destination (not to you!).
It is completely appropriate, if not expected for you to include your application materials in your email to the recommender. Things like your personal statement, or statement of research interests would be helpful. Probably not things like your transcript- the whole point of the letters of rec. is to get beyond the performance indices, and provide a more human evaluation of the applicant.