>>1 As for my own suggestions. I don't know you well, but I assume you're pretty young, so this is just a loose list from a chick of what will help girls trust you a bit more.
To keep girls from being turned off by you:
1) Try to take care of yourself. I'm not telling you to gain or lose weight, but make sure your hair is well kept (preferably styled well if it's long) and your skin isn't oily, etc. Wear clothes that fit, maybe even try to match them well. Girls appreciate someone that can take care of themselves to a degree even if they're not super attractive.
2) Be confident when you can without being egotistical. This is a big to a lot of girls. They may be willing to help you with your problems, but most people (male or female) don't want to date someone that's not well off mentally. They don't want to be the 'mommy' of the relationship to make you feel less depressed (unless they have a thing for that which some girls do). Confidence also gives you a natural +10 attraction. When you walk like you know where you're going, talk like you know what you're saying, etc. it helps them feel more comfortable with you.
3) Don't be a dick to chicks just because your guy friends are around. This includes rating girls appearances, making fun of girls for their clothes / makeup / weight, picking on certain girls in the class, etc. Girls do it to other girls but often feel threatened by a guy that will do the same. Just because it's only you and your friends in the corner doesn't mean nobody will overhear it. Some ladies will put it to the side if you're exceptionally good looking, if you were close friends with her from the start, or if they liked you before they found out about you being an asshole, but don't rely on that being the case.
4) Don't publicly obsess over your interests. If the only thing you wear are t-shirts with animes / videogames on them, or if you always seem to talk about or do reports on the same things over and over again, etc., it turns most people away unless they're also really into those things. It's not always because they think you're weird for it, either; it makes you seem like the type to brush off other people's interests, and the last thing you want in a relationship is to be unable to talk about things that you're into. Try to keep it in check.
Now, to get girls to go out with you:
1) Figure out your type. What traits do you love? What traits do you hate? If you can't handle a girl that talks a lot, then don't go for a girl who talks a lot. That type of thing. You want to have standards.
2) Observe the girls that interest you (without stalking them). If they're a little more outgoing, you might want to try adding them on social media to get to know their interests better. That'll let you engage in casual conversation later on.
So now you know her, and she should have a vague idea of who you are.
3) Become friends. (This isn't always a step. If you find that she's really interesting and would make an amazing friend, then go ahead and try to be friends with her. Do NOT do this with the intention of going out with her. Do it because she's someone you'd want to be friends with. If you think she wouldn't be good as just a friend, then skip to 4.)
4. Ask her out. Seriously, just ask her out. If she says no, then move on to another girl (preferably someone she's not close to). Rinse and repeat. You'll find a girl who'll say yes eventually, and after you've dated some, you'll find someone worth staying with for a longer period of time.
Some guys like to put in the 3.5, which is an obscene amount of flirting. Please don't do it unless it's a girl that appreciates it. There are a lot of girls that get offended by flirting and will immediately remove you from their potential candidate list. However, if you're willing to take the risk, I'm sure there are others who will appreciate it, and it may increase your chance at someone saying yes at point 4.
Good luck o: