[Heisenberg97]

I know you have to consider the symmetry elements and can deduce from a chart which point group you're going to get.
But how do you know if Cn has nC2 perpendicular to the Cn axis of rotation?
And how do you know if the molecule has a horizontal or vertical mirror plane?

[flick-a-bic]

Until you get really good just follow a flow chart like this http://chemwiki.ucdavis.edu/@api/deki/files/17590/=Sym1.jpg.bmp?revision=1

As far as nC2-- this is a 180 rotation (360/2) Just build a model and see if you can rotate the model 180 degrees and get the same model back. Practice doing it in your head.

Horizontal plane is along the x-y plane.

Vertical Mirror plane contains the entire z-axis.