I agree with the above poster clienk. I'm going through the same process too. I'm applying for a internship at a cancer research center that's known in my state. It's hard, but you really have to sell yourself. Researchers want someone who will dedicate their time for research and a student who will put themselves out there and do their best. There's no shame emailing professors and asking, the worse thing they can say is no. Some professors love how students are willing to step up to the plate. A resume is really nice, it doesn't have to be super perfect, type up a resume like any other. Include name, address etc., typing speed, job skills, computer skills and etc. You should also include a personal letter that sells you. This should include your academic outlook, career goals, reason why you would want to intern, hobbies, and information that shapes you as an individual. You can show your test scores and stuff like that if you want to. It's not like you are competing against 100+ or even less than that.
I hoped I helped, good luck.