How do you approach someone to ask for a letter of recommendation?

I am applying for some scholarships that require three different letters of recommendation. I know two will be easy as pie to get but for the third I would like to ask one of the top brass here at work and possibly the head of the department where I am studying. How should I go about making the request? Should I write a letter? Call them? Set up an in person appointment? Any ideas about what I should say? I am sure at their level they are used to these requests and comfortable turning them down, but man oh man, I will be so horrified if they say no!