Group algebra, cyclic group, ring isomorphism

Question

Consider the cyclic group $G=\langle g\mid g^{3}=1\rangle$,his group algebra $\mathbb{C}G$ and $\mathbb{R}G$. As a complex algebra, how to construct an isomorphism between $\mathbb{C}G$ and $\mathbb{C}\times\mathbb{C}\times\mathbb{C}$? I also want to know all irreducible representations of $G$. Is there ring isomorphism $\mathbb{R}G\simeq \mathbb{R}\times\mathbb{C}$?