Letters of recommendation are often required for graduate programs, scholarships, and fellowships.   Since these letters take time to compose, request them well in advance of deadlines.  Letters of recommendation are not required for internships, co-ops or entry-level jobs. 

Who to choose to write your letters?
Choose those who are most familiar with your academic performance or research abilities and interests.  Faculty would be a first choice.  

How to proceed
Make an appointment and ask if they'd be willing to write a letter of recommendation.  If yes, provide a copy of your resume and a description of the opportunity to help them write a strong targeted letter. Email a note of thanks and keep them up-to-date on your progress.