Show your genuine interest
Everyone likes to feel valued and appreciated. When you see something you like and admire from your potential mentor, let them know and be specific. Follow up by asking if they would be willing to discuss things further over a coffee, show your genuine interest in learning more from them.
Have your selling points
Send an email that explains who you are, what sets you apart from others, and what you hope to get out of the meeting, so the expectations are transparent and your mentor is more likely to agree to share their time.
As tempting as it can be, according to the experts at Bumble don't use the 'm' word outright, at least at first, as it closes off the potential for a naturally built rapport. Instead, suggest that you would like some guidance in your career trajectory, as you admire the pathways they have taken.
Be open in regards to scheduling, they are giving you their time, make it easy as possible for them to arrange this.
Keep it succinct
Be respectful of the value of time. Thirty minutes is a reasonable amount of time to ask for and make sure to keep to the allotted time when meeting, to increase the likelihood of them wanting to meet again in the future.
Get straight to the point
Don't waste time with small talk. Let them know why you admire them, and what drew you to want to learn from them. Do your research, know their background, and have questions ready to ask.
You are here to learn and grow from this person, make sure you are attentive, and keep the conversation focused around them.