Open your mind- If the people in your life have always been meat eaters, try to put yourself in the shoes of your date and see things from their point of view. You may not agree, you may not want to join her in her way of life; however it's important think outside the box or you won't get anywhere fast. She was likely a meat eater at some point so she can probably imagine how it feels to be you.
Vegan on Female First
Research restaurants- Menus can be really restrictive for vegans if you pick the wrong place, so make sure that if you offer to take her out she can have more than a side salad and water. Or ask her- she might know somewhere really good so you can try out her normal cuisine.
Find out what you have in common- You may not be a vegan, however there are lots of other things you are bound to share a passion for. Explore subjects like hobbies, social habits, books, TV shows, movies and you will land on something.
Talk about your favourite foods- You may also have some favourite foods in common- like pizza, pasta, burgers- all of which can be veganized of course. If she hints at some of her favourite snacks it won't do you any harm to have some lying around the house next time she comes over.
Watch documenters together- Movies are great, TV shows can fill an hour or two- but why not learn something together by watching a documentary? Even if you don't agree it will give you something to talk about afterwards.
Forks Over Knives, Fat, Sick and Nearly Dead and The Cove are a really good place to start.
Buy her dark chocolate- Most dark chocolate is vegan so get her a bar next time you see her so she knows you've been thinking about her.
Talk about unrelated things- Vegans don't want to talk about being vegan 100% of the time- they have other interests and want to do things other than slaving away in the kitchen or talking about it.
Do stuff that doesn't involve bringing the subject up- take a walk, go for a run together, do some yoga a bike ride- anything to embrace the more physical things you can do as a couple.
Buy her some Kombucha- For those who don't know- a slightly fizzy black or green tea. Have some in your brew cupboard and you will score some brownie points!
Be supportive- Vegans can get a lot of backlash from people who are uninformed, so make sure you stick up for her if she gets some stick and be considerate as much as you can. It means a lot to her, by showing her you acknowledge that will bring her closer to you not push her away.
Don't introduce her as a 'vegan'- She can tell people in her own time if she chooses. It sets the tone for evening and if it's with people who don't approve or who dismiss veganism it can make the night really awkward.