Here are the three cases of horizontal asymptotes:

1) If the degree of the denominator is greater than the degree of the numerator, the HA is y=0

2) If the degrees of the numerator & denominator are the same, the HA is the ratio of the leading coefficients

3) If the degree of the numerator is larger than the denominator there is not a HA

In terms of finding which it is, you can factor it all out and see what the degrees of each will be.

Hope that helps!