I know that Graph Isomorphism should be able to be verified in polynomial time but I don't really know how to approach the problem. Any help would be appreciated.
You haven't explained what graph isomorphism means for you, so let me assume that you mean the language of all pairs of graphs $(G_1,G_2)$ which are isomorphic.
Two graphs $G_1 = (V_1,E_1),G_2 = (V_2,E_2)$ are isomorphic if there exists a bijection $f\colon V_1 \to V_2$ such that $(x,y) \in E_1$ iff $(f(x),f(y)) \in E_2$.
You take it from here.