Making a capacitor is fairly easy, however I won't go into full details here - you can look it up on the web - search for "leyden jar".
The plate thickness affects both the capacitance and maximum voltage. As plate thickness increases, capacitance decreases, but maximum voltage rating increases. These values are also affected by the type of material used for the plate (eg, plastic or glass).
Generally, a homemade capacitor will not have a polarity. The only polarised capacitors are electrolytic and tantalum types.