A great way to ask for a letter of recommendation is to give a lot of details when you make the request. Be specific. What are you asking for a letter for (do you have a specific job you'd like to be recommended for, or is it just a general letter)? If you have a job in mind, give the recommender details of the job you're applying to along with a summary of why you think you would be a good candidate for the job.
Remind the recommender of what you accomplished when you worked with them. It helps to keep a list of your projects/accomplishments as you go, so you can look back and pull out highlights of your time as a volunteer or employee. It helps to remind them of your value, so they can mention these specifics in their letter.