When approaching faculty for recommendations for fellowship applications, remember that the recommendation letters provide a unique space where aspects of your character not otherwise apparent in your paper application can be highlighted. For this reason, it is best to ask faculty members that have both taught you and gotten to know you as an individual. Faculty members ideally should be able to speak of your many dimensions, your breadth of intellect, and your individual interests in a way as to set you apart from your cohort of undergraduate peers. For this reason, your breadth and depth of rapport with, rather than prestige of, the faculty member should be the priority when asking for recommendations.
When deciding which faculty members to ask, also consider the goals of the fellowship. Recommenders should be able to speak to what the selection committee sees as the values embodied in the fellowship. Along with a copy of your CV, personal statement, and research proposal, give recommenders a brief description of the fellowship that you are applying to, and remind them that they should address the values of that fellowship. Do not forget to write them and say thank you for writing on your behalf. This should be hand written, not emailed. People appreciate being recognized for the time and energy they expended in supporting your candidacy. For this reason, too, you should keep them apprised of how you fair in the competition.
Office hours are the best opportunity to get to know your professors outside of a classroom setting. Take advantage of these hours during the semester to get acquainted with a number of your professors and to build relationships with them as mentors in your field. Each relationship you build with a faculty mentor will enrich you as a critical thinker and foster your curiosity as well as increase your ease with rigorous, academic conversation. In this way, relationships with faculty members benefit you both by making you a more thoughtful and directed student as well as by preparing you for fellowship recommendations and interviews.
Although most fellowships desire only faculty recommendations, some allow recommendations from others who can speak about non-academic skills, such as leadership ability or public service dedication. For these fellowships, you may ask internship, employment, or volunteer supervisors.
Oftentimes students ask if it is possible to use graduate students as recommenders. Because fellowship committees see graduate students as students not unlike yourself, you should only get fulltime faculty members as recommenders and avoid graduate student recommendations.