Make it your goal to build a long term relationship with the mentor instead of focusing on what you can get from the person in the first meeting. Most importantly, make it easy and rewarding for the mentor to help you. Since you’re likely dealing with a very busy person, don’t ask for coffee or lunch. Instead, offer to come to their office for a 15 minute meeting. Do your homework in advance, and arrive with a short and specific agenda that leverages the relevant experiences of the mentor.