How to write an interview application if you're applying through connections?

It's been hard trying to get an internship in this area, especially since I'm a foreign student. That's why my dad has asked his friend whether or not I could send in an internship application to his company, and he replied yes. My dad screenshotted me a general company email address from their website after that. I feel awkward... Do I just send a regular cover letter? How should I even bring up the connection (or should I even bring it up?)

Edit: I don't think my dad's friend is in HR, so I'm quite unsure.

Thanks for the help! I'm not very proud of this, but I really do need the experience.

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