There's a great explanation of this on the HowStuffWorks website, and the NASA site has good material too if it's space-related. Both are written for normal people, not scientists, so you won't get lost in jargon.

I'd recommend the book 'A Brief History of Time' by Stephen Hawking, or for the math side, 'The Joy of x.' Your library has them. They're written for curious regular people. You don't need a degree to understand the big ideas.

Be careful about 'common sense' here — a lot of science is counterintuitive. The whole point of doing experiments is that the universe often doesn't work the way our gut tells us it should. The Earth feels flat and stationary, after all.

I'm a physics grad student and this is one of my favorite questions to explain. The key insight is that our everyday intuition doesn't always apply at extreme scales — very small (quantum), very large (cosmological), or very fast (relativistic).