Find a set of generators and relations for Z/nZ (integers modulo n).
I think it is <a, b | a^n = b^n = 1, ab=ba> but I am not positive. Would this be correct?
No - this group is two-generated while $\displaystyle \mathbb{Z}/n\mathbb{Z}$ is cyclic. Basically, you are looking for a one-generator group with the property that the generator to the power n is the identity. You do not actually need the commutator ab=ba there - this follows from the fact that your group is cyclic. So, plug these two stipulations into a presentation and see what you get...