Re coming home the next day: Keep her in a small, quiet, warm room confined for the first 24hrs but keep an eye on her. Provide her with plenty of water and a little bit of food but don't worry if she doesn't eat. Keep a really close eye on her stitches - if she pulls or licks at them, get a head collar for her to wear. She should be fine after a couple of days, just try to keep the wound area clean and un-interfered with so the vet or nurse can see the wound 10 days - 2 weeks later and take the stiches out. In my experience, Tiger's purrsonality changed from an outside/wild cat to a very affectionate, charming young lady

Also just remember to give her a light meal the night before, and take away water from the time you get up. Kittens have a fast metabolism so she should be allowed to have a small amount of food and water the night before the op.

And definitely follow your vets instructions!

6 months is a good age to get your kitten spayed, so well done on taking that initiative
Tell us how she gets on!