That is a vital question, indeed!
I only know a few dishes and am kind of a picky eater, so if I'm cooking for the girl it's chicken. Chopped chicken, with Greek seasoning plus salt (ideally, sea salt), fried in a skillet with butter. And I'll make a side of potatoes. Generally a pretty safe dish.
You should give the girl the option to choose what you'll make. That way she can either tell you what she loves, or at least veto things she can't eat. You don't want to slap a steak on her plate, only for her to not eat it because she's a vegetarian and just didn't want to mention it and rock the boat. So "It's up to you. Either I can cook you some delicious chicken and potatoes, or, I'd love this just as much or more, if you're up for it, you can cook something, and I'll assist" often works great. She'll make what she likes, and it gets her more invested in the date, because she contributes so much more toward it.
Wine works great if you don't want to mix drinks. Keep a bottle of red and white wine on-hand, since some girls have a preference. And keep glasses for each (there are different wine glasses for red vs. white wine). You can teach her how to swirl her wine in the wine glass if she doesn't know (many girls don't), and that's a fun little thing. Wine really helps to set the mood too, of course.
I know guys who are excellent chefs, and use that to make dinner dates even easier. They just talk up what outstanding chefs they are, talk to the girl about some of their best dishes, and invite her over to cook something she shows interest in or tells them she'd like to try.
I've not done the "let's make desserts together" bit... I'm a little careful about desserts, since you never know which girl is on a diet, or who's on a crusade against the sugar industry. But if you've established she likes desserts, and she isn't going to feel bait-and-switched because she was hoping to get properly fed with a meal, I could see that doing well. A piece of chocolate cake drenched in raspberry sauce, or a chocolate mousse with whipped cream, either one served with some wine, could be real good. Chocolate + wine is a nice combo.