Get to know your faculty members and let them get to know you. They can write a specific, detailed letter that speaks to your accomplishments. You can build a relationship in a variety of ways:
Request letters of recommendation at least a month in advance of the deadline, preferably 2-3 months in advance. You can send a reminder to the letter writer closer to the deadline.
Be professional in making the request, but don't feel awkward about it. Faculty members and former employers want to support their students. They are accustomed to writing letters of recommendation. Provide them with as much information as possible to help them write the letter and be sure to share information about your proposed program or activity. A draft of your statement of purpose, application, and copy of your resume is helpful, so they have a full picture of what they are supporting you for. Establishing a portfolio of your work is helpful to share, to refresh their recollection of your skills and abilities.
Request letters from only faculty members. Letters from colleagues or employers should be requested in the very rare case when your proposed study is extremely well aligned.
Graduate School: Be proactive about gaps between when you graduate and when you apply to graduate school. The best letters of recommendations are from faculty who know you well. But because they teach hundreds of students, it is harder for them to write strong letters the longer it has been since you were in their classroom. If you have a gap between graduation and applying, consider requesting the letters while you are still fresh in their memory and keeping them on file.
Request letters from a combination of supervisors and faculty members. These individuals should be able to speak specifically to the work you have done and connect it to your proposed work.
Send a thank you note and update them on your progress. A good reference writer will be interested in your success. It will also help next time you might need a reference from that individual.