The best letters come from people who know you best, who have seen firsthand how dynamic, brilliant, committed, passionate, or effective you are. Their position or title is less important than their ability to give detailed examples of just how fantastic you are.
That said, the letter writer should have the experience to speak authoritatively about how remarkable your qualities are. A graduate student, for example, is rarely qualified to do this.
Be sure to follow the individual program’s guidelines for the number of required letters and how many of those must come from faculty.
You should contact potential recommenders as soon as you think you are going to pursue an application. Ask for the recommendation at least a month in advance of the deadline. Schedule a meeting with the recommender and come prepared.
Maybe you’re an online student, or maybe you’re just shy. Maybe you’re in a program with enormous lecture classes and no real opportunity to work in smaller groups. In all these cases, you will need to work a little harder to forge relationships with faculty as far in advance as you can. Visit potential faculty recommenders during office hours or set up appointments to meet with them. Explain what you are thinking of doing and ask for their honest assessment of your candidacy. You might ask, too, whether they would feel comfortable supporting you in your efforts.
If you don’t have other options, you might acknowledge that to the recommender, and ask if there are ways that you can help them feel comfortable writing a stronger letter.
Be sure to include non-faculty members in your pool of potential recommenders. Depending on the award rules and criteria, a work supervisor or student activities advisor is often (but not always) an appropriate choice.
Each program has its own rules, but generally speaking you may only submit the number of letters that are requested. Look carefully at the program website for clarification.