How do catalase and other antioxidants neutralize free radicals?
Catalase (hydrogen peroxide oxidoreductase) does not actually quench free radicals. It catalyzes the conversion of hydrogen peroxide to water; the former is a source of a free radical, not a free radical in itself. 

This is the proposed mechanism of action of catalase: First one of the oxygens is deprotonated by at the active site of the enzyme. Then the Iron atom that is bound to heme forms a co-ordination complex with the deprotonated oxygen and pulls it away from the other oxygen. As a result the O-O bond breaks. 

Free radical quenchers/antioxidants react with the free radicals and form non-toxic products.