What are ways a mother and father can help their teenage daughter with a successful sleepover?

Trust her to act responsibly, and show her you trust her to act with responsibility. Tell her she will never have another sleep over, nor ever attend one, if she doesn’t. Then leave her to the event. (Of course, be there for her as support, if she needs you.)

Tons of candy and movies. And leave them alone…...although grilling hot dogs would be cool. Then leave them alone.

Yes, help with the planning and provision of food. Talk to your daughter about planning some activities – videos, games, dancing, etc. – that the kids can do. Help plan in advance the sleeping arrangements. Set a time with your kid in advance when you expect them to be (relatively) quiet. Lock the liquor away.

And ,,,stay home but out of sight as much as possible.

I had a party once. I think I was 16. The phone rang. Kids picked it up and passed it around in a circle as everyone said “Hello?” Dumb. Anyway, then they gave me the phone. I said everything was fine. Kids wanted to know who it was. I told them it was my parents.
The basic reaction was “Oh shit! Do they know you’re having a party?”
I said, “Well, yeah. They’re upstairs.”!!! LOLL!!

There was a way to call your own number from an extension to make the phone ring, but I forget what it was.

@Dutchess_III has an excellent point. The best parents are either not seen but there, Or there and accessible but definitely in the background. And the idea about grilling hotdogs, or even something better, then disappearing to the background or .more private places of the home, is pretty cool

Set a budget, do she can understand the need to limit the number of guests.
Sometimes lots of extras get invited because peer pressure will be used to be added to the list. With a set budget, invites won’t get out of hand, and the question of why can’t we grill ribs instead of burgers is answered.