I was involved in three summer programs as an undergrad and currently help review applications for my school's summer research program.
Here are a couple things that we look for and I know other programs do as well:
-GPA: There is usually a minimum cut-off which varies from program to program. At my school the cut-off is 3.35, for the programs I did as an undergrad the cut-off was a little higher (around 3.75).
-Research Experience: Many of these programs are made with the intention of exposing undergrads to research, so many times prior research experience is not required. Having some research experience and demonstrating that you are serious about it, and can commit yourself to 10 weeks during the summer, helps a bit. However, applying with 2-3 years of research already is not necessarily a must.
-Personal Statement: Explain to us why you are interested in doing research during the summer. How will research help you in the future (decide between grad school and med school, you are interested in learning more neuroscience in lab, you took a biochemistry lab at your school and want to delve deeper into it, etc...). Some programs also have a diversity outreach component to them, our program does. A big part of who we will consider comes from learning about adversities that the student may have faced and them telling us how they will diversify our program and academia.
-Letters of Rec: Probably the 2nd most important after the personal statement. Since you mentioned you have no research experience, perhaps getting a letter from a professor you took a lab class with might be best. If you took a lab class and enjoyed it, was active in class, you can weave this narrative into your personal statement and a letter from that class' professor will be good to back up your claims. Other letters we like are from people who can vouch for your persistence (which you need in research), curiosity, team work capabilities and academic performance.
-Extra Curricular: This is somewhat specific to our program since we focus on diversity outreach, but I think it can apply for other programs as well (it helped me as an undergrad). Activities that demonstrate your involvement with under represented communities in STEM , such as tutoring high school kids, being part of your local SACNAS chapter, etc..., are valued greatly, specially if you were a leader among them.
I know some programs also screen for applicants who are only interested in getting research experience so they can apply to MD only, so keep that in mind if your narrative is very MD oriented.
Happy to answer other questions.