We will review the basic theory of Chow groups and study its intersection product for simplicial toric varieties. We will show that the Chow group endowed with the intersection product is isomorphic to the cohomology ring, thus showing various corollaries such as relating Betti numbers and the number of cones in the associated fan. Finally, we will show a description of the cohomology ring in terms of generators and an ideal of relations. We will also prove analogous but stronger statements for nonsingular toric varieties.