I heard that most of the quality of the tone in a guitar comes from if the top is solid or not. How much of a difference does it make if the back and sides aren't solid wood?
A solid back makes a very big differance. There is a bit of debate about whether solid sides make much of a differance.
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^--- there are alot of people that agree with ben on this issue... and then there are alot of people that say all solid is the only way to go. it's just whatever you think really.

as far as there being a huge difference in sound, between solid and laminate sides... i think the difference would be pretty negligible when all other aspects of a guitar are constant. a solid back does alot more for tone, though it's not nearly as big of a difference as there is between solid and laminate tops.
the material you make a guitar out of is mainly preferrence composite acoustics makes guitars entirely out of carbon fiber and they sound fantastic they dont have the booming bass of solid wood guitars but tell me another acoustic you can leave in your trunk it 10 below weather bring it inside to 75 degree house and have it sound perfect or have a 200 lb man stand on it then play any scale without being out of tune so it really doesnt matter about material but a solid top and a solid back is key to good tone on any guitar