How to get girlfriend to start eating better?

It's her business. Instead of telling her what you think she should do, talk to her about what you're doing. Don't say "you need to learn to cook and eat healthier, Jane." Instead, you say "I've been teaching myself to cook so I can eat healthier. I really don't want to live on fast food. It's not healthy."

Lead by example. Don't constantly shove your behavior in her face, but make it clear you're taking steps to look after your health and your weight, and that you worry about so many of your classmates who seem to live on nothing but fast food. She'll either take the hint and think about her own lifestyle, or she won't care and she'll continue doing what she's doing now.

You could also encourage her to let you cook for her, and then get her to help out when she's at your place for dinner. Offer to go grocery shopping with her to pick out stuff she can keep on hand or offer to come to her place and help her cook.

instead of telling her what she's doing wrong and how, in this subject, you clearly consider yourself her superior, how about you just invite her over to make dinner WITH you. Like it's a fun thing to do together instead of you trying to improve her.

Get her involved. Maybe see if you can take a local cooking class together, or watch some cooking shows together and then cook the dishes together.