How does friction actually work at the molecular level?

The key thing is that friction isn't about surfaces being rough - it's about electromagnetic forces between atoms that get pulled into contact. When two surfaces touch, their atoms don't actually meet flat; instead the high points (asperities) press together and create van der Waals forces and sometimes even temporary chemical bonds. As you try to slide one surface over the other, you're literally ripping apart and reforming these tiny atomic connections thousands of times per second. That's where the energy goes and why things heat up when they rub together.