how do I speak with a manager on-site?

You have to speak to the manager when you are there. If you have a problem.

In-N-Out does not make their phone number public which is the industry standard for fast food. To speak with a manager, you are going to l to physically go back to the restaurant and ask to see the manager on duty.

Ask while you're there or call the restaurant if you've left.

Basically ask who is the manger on duty and if you are able to speak to with them.

You ask to speak to the manager on duty.

I would just politely ask to speak to the shift manager.