There is a book I have which is a very usefull basis for helping to understand ground planes amonst other things. It is written in very simple language well worth having as a reference book.

Henry W. Ott. Noise Reduction Techniques in Electronic Systems . its old and should be in every college library, if not snap up a second hand copy will only cost you the price of a beer

Placement and sizeing of ground planes and vias can get quite fancy, especially with multilayer boards, You can't just slap one on either side, it can do much much more harm than good, on a simple double sided board one only has to consider problems created by orphans (areas isolated by components).

Take a look also at ground planes around external timing crystals and "rings" you may get some extra marks.

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