How can the electric field formula for a parallel plate capacitor be derived?

[Fluxxx]

For a parallel plate capacitor, the electric field can be written as
$$E=\frac{q}{\epsilon_{0}A}$$
In my textbook it doesn't say how this is derived. I wonder how it is derived - i.e. how can one get to this equation from simpler equations?

 

[e.bar.goum]

Use Gauss' law to find the field for a sheet of charge, then consider a capacitor as two plates - add the solution.

( http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elesht.html, but you should try and do it yourself)