You are a helper. That's your job.
If she needs a blanket, get it.
If she wants another pillow right when you get back....Don't give any grief, just go get another pillow.
If she wants to see the nurse, get the nurse. Don't try to say "oh, they'll be in here in a minute, just step out quietly and tell the nurses station (don't snag a nurse in the hall...they're probably busy and whatever your wife needs is being monitored on the little display)
Stay out of the way. Tomorrow is going to be easy for you. You're not the one in pain, you just stand there and look pretty. You're there for support, not to deliver the baby. Tomorrow is (likely) going to be a long long period of anxiety and waiting....followed by an hour of super high intensity and a dramatic conclusion that's going to completely wreck your wife (in a good way) she'll have pushed out a child, her body is going to be up most of tonight, lots of anxiety and waiting tomorrow (with contractions all damn day) followed by 10 rounds of boxing crammed into a 1 hour non-stop session. That said...get her what's food she wants. She's gonna be hungry as hell when she comes around after the post baby nap.
Encourage her and be there for her and just be a "yes" man (unless it's something serious) pillows, food, naps, frequent trips down the hall etc are not serious issues...let those go.
When the doctor does come in, and it's game time...try your best to be out of the way and be there for her. That's your focus. You're not going to find anything in there that the doc isn't going to see...let them handle it.
Also...there's no preparation or videos that can prepare you for what you're about to witness. It's simply amazing and exciting...just remember, she needs you there.
If family is showing up, ask who and when they can be brought in. Maybe mom wants to be in there but she doesn't want that...you're gonna have to be the body guard. If you don't want mom in there...doesn't matter. Suck it up.
Don't get caught taking a nap before the baby is born. Just be available and out of the way.
Best of luck and congratulations