I love movie dates.

Since it is your 1st date: Just use the movie to build comfort and connection.
Just sitting next to each other for nearly 2 hours makes her feel comfortable spending time with you.

Don'ts:
When you meet at the cinema just do nice smalltalk, nothing big.
When the movie start, just shut up. If she comments the movie during the time, than you can too. But keep the balance. If she don't talk, than you don't talk. Most people enjoy movies silently.

If there is a sex scene, it gets maybe awkward. But this is actually a good thing.
Every emotion is good, as long as she thinks the time with you was good.

Don't use the lack of light to stare at her.

Dos:
Try to be silent at in the cinema (not everyone should hear what exactly you are eating). Some girls get embarrassed and they don't want to disturbed other people.
If you are silent, she usually tries the same. Nag her if she doesn't succeed. ^^

Most Important: Talk about the movie when you left the Cinema.
Ask if she wants to join you for a drink/coffee/whatever and talk about the movie!
Ask her what she liked, what she didn't, etc.
Tell her what you liked. You can quote or act as character in the movie.

Try to find something you both liked. Use it to build a connection!

Next: If you are seeing her again, use the connection you build and refer to it.
Use the movie for running jokes.
The best ones are the ones only you two understand. This gives you two a strong connection.

BTW: Be sure that you got enough IOIs to kissclose. Depending on the culture flirting and nagging is intense enough and a kiss on the 1st date could be to much. If you are unsure, go for the byebye-kiss on the cheek.

Flow

Are you paying for her movie ticket?

If so, she could be using you for dates and she will say what you want to hear to make you think she is attracted to you.

Jesus dude, just fork over the ten bucks for the movie. It's not like you're spending €100 on her for a dinner date. Don't be cheap or listen to that bullshit of "Don't pay for a chick ever" because it's the most stupidest shit you'll ever hear or do. Women remember this shit and will hold it against you big time. They won't see you as being cool or independent, they'll just see you as cheap and here's some news for you: Women don't like cheap guys.

What you can do, however, is pay for the tickets and have her pay for the popcorn(Like €5 if even). She'll put up a bit of a fight out of decency on the tickets(Just means she's a nice girl and not a bitch) when she does just level with her "Tell you what. I'll get the tickets, you can get the popcorn. Sound like a deal?" She'll say "fine" then you can mess with her and say stuff like "Better be the best damn popcorn i've ever had. Make it count." Say it in a joking way so as not to insinuate she owes you -- seriously -- for the tickets. You can make the whole interaction fun this way and take the pressure off/break down any awkward barriers with this little bit of banter. If you're in the mood link arms with her if that's your persona.

Now, Flow is spot on about women who use guys for dates -- I have close friends who do this very thing -- but if it's for the sake of a cinema tick or a sandwich it's not really worth it coming across as cheap which is why you never take a chick out for something expensive on a first date or until you get some physical investment(Kiss, etc.) to show she's serious about seeing you and not just in it for a free meal. After she gives you that then you can safely assume she's not just using you.

So, pay for her ticket. Whenever you're going on first dates go for walks, pubs or other cheap but nice things that you wouldn't mind spending €10-20 over. It pretty much eliminates her seeing you just for free stuff and you can still have a good day out.

Never pay!

If she thinks you should pay, you can tell her with a big friendly smile:

"I never pay for a girl!
I know that some bitchy girls make needy nice guys pay just for their own benefit.
But I am not a needy nice guy and you're not a bitch, right?"

Even if she is a bitch, she will pay for her self.

The best first date is really a coffee shop or something, to get her life story.