It's a case of playing around a colour wheel is a good starting point to see what colours go together.
Chestnut Products do a range of spirit base stains and Liberon do a pack of water based dyes I think that the water based dyes mix better if you want to make up various tones of one colour but water based colours take longer to dry than the spirit base colours.
A trip to you nearest art shop is also a good idea there's all sorts of goodies that you can pick up.
Applying the colours can be done by brush, cloth, air brush and many other things, all give a different effect.
It's also a good idea to test what you are using on a a off cut of what you are turning to make sure that the dyes or paints that you are going to use look right on the wood.
Hope that helps a bit.
All the best
Ed