How do you politely ask for a day off?

You politely ask for a day off by using professional language that makes a request instead of a demand. While you may have the right to use your vacation days, asking your boss about using it is much more professional and polite than telling them you're going to be gone.

It's courteous to say something like, "I have a week of vacation that I was planning to use this summer. Would it work for me to take June 20-25 off?" This is an assertive way to tell your boss that you're going to take a vacation while still politely respecting their authority and their need to coordinate their employees'schedules.