Prove that the ring of integers contains a non-trivial unit

Question

I want to prove that the ring of integers $O_K$ in a real quadratic field $K$ contains a non-trivial unit. I'm given the hint that I should use a theorem concerning lattices and convex sets. This seems pretty clearly to be pointing to Minkowski's theorem on lattices. But I don't really see how that can be applied to finding units.