I'm just your average home gardener, not a soil scientist, so I tend to go by several times as much brown (by volume) as green, as a general rule of thumb. But IMHO it's not rocket science. If it isn't heating up, try more greens and more moisture. If it is getting slimy or smelly or nasty, add more browns... It will compost, pretty much whatever you do.
Here's an article about it, that suggests anywhere from 5:1 to 8:1 brown to green ratio by volume: