If you are starting a stranded pattern (such as Fair Isle) you can generally just start knitting with the new color since it starts near the beginning.
For intarsia, you can twist the end of the new color with the main color for a few stitches before you start with the new color. After that, as long as you hold the color you're stopping over to the left as you pick up your new color, they will be twisted and not form a hole. When you are done with a color, twist it in with the color in use for a few stitches and leave a tail to weave in later.
I like to twist the yarn in when I'm done with it so it's secure and I just have to take care of the hanging end with a quick check/stich when I'm done.
Some sites say to just tie a knot with a tail to weave in later.
Hope this helps!
"Trust the pattern!"
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IngridKH on Ravelry