It’s always a smart idea to offer to write a letter of recommendation for a colleague who you know is well qualified for the job in question. Consider it good career karma; after all, you never know when you’ll need a letter of recommendation for yourself, and your colleague may be happy to return the favor.
How do I approach potential letter writers? First, make a list of professors and/or supervisors who will be your best advocates. Then, set up an appointment to discuss your request in person. Do not make the request via email. Be prepared to articulate your interest and reasons for attending graduate school. Letters of recommendation are written strictly on a voluntary basis. The best approach is to ask potential letter writers if they are willing to write you a strong letter. If you sense reluctance or the answer is no, ask someone else.