I agree with Antares that it depends on the project. Each technique is useful and fun to learn. Find a pattern that you like and try one of them out.
In many patterns, the cast on and ribbing or border are done in one of the colors and the other colors added for the main body of the project. Starting a new color is just a matter of holding the end of the yarn in place with one hand and beginning to knit with the new color. There are videos here for intarsia
and for fair isle
. You can see that one of the main tips in both is to cross the colors so that you don't get holes where you've change colors.
Good luck choosing a pattern and come back if you have questions!