Most of the research I did during college took place in my classes. How can I leverage this when applying to grad school?
Research experience in classes should show up in recommendation letters from the corresponding faculty (and in your personal statement, but the former is much more impactful). If you've done high-quality and nontrivial research in your classes, then you should make sure to pick recommenders that can talk about and vouch for it. 

In fact, research experience at dedicated RA positions shows up in pretty much the exact same way. Just listing an RA position on a resume does very little; the real value is getting a good recommendation letter from someone who knows you well and is familiar with your work.