How much agar for my petri dish?

All you need to do is cover the bottom of the dish. How little agar this requires depends on your skill at pouring it. The art is to "swirl" the dish so that the agar spreads over the whole dish, requiring less agar per dish.

With straight pouring, most people need about 10ml. With 'swirling' I can easily manage 5ml.

I like G0rdi's answer. 10 mL is usually a good amount - I prefer not to do less than 10 mL myself.

Do not try to make it too thin though, as the agar can more easily dry out and burst if the layer is too thin. Make sure the bottom is covered.