It's all described in the Configuration Options section of each chart documentation page (see
LineCharts as an example). Here's an example showing both methods for assigning colors to a LineChart:
http://jsfiddle.net/asgallant/EuvJc/. The example also works exactly the same way for
AreaCharts,
BarCharts,
ColumnCharts,
ComboCharts,
ScatterCharts, and
SteppedAreaCharts.
CandlestickCharts work similarly, but have more extensive color options.
PieCharts also work similarly, but they don't have the series option available.
BubbleCharts can be colored the same way, but the can also be colored by point value instead.
GeoCharts and
TreeMapCharts can only be colored by point value.
GaugeCharts have options to color data ranges on the gauge, not data points.
Most charts assign a single color to each series (exceptions are PieCharts, where each row get it's own color; GeoCharts, TreeMapCharts, and BubbleCharts set to color by value; and GaugeCharts). If you need to be able to assign different colors to data points within a series, it is doable under certain conditions, but unless you need it, it's probably not worth going over.
I know it can seem a bit intimidating, but the API is actually pretty simple to use. I'm more than happy to help you get started. Feel free to ask any questions you may have and I'll do my best to answer them.