The most common answer: Practice. Start practicing slowly and gradually increase your speed. Make sure to practice so slow that you can play each note cleanly. Remember, practice makes permanent, not perfect. If you practice playing sloppily, you become good at playing sloppily. If you practice playing correct every time, you become good at playing things the right way. You may also want to check out Lisa McCormick's Acoustic Finger Picking tutorial for the basics: http://www.guitartricks.com/tutorial.php?input=596
This only covers the basics, but I'm pretty sure she has more tutorials on the subject. If you have any questions, I'm sure Lisa can answer them. She is probably the most talented acoustic guitar teacher you'll find :)

Also, you don't necessarily have to be able to use finger picking just to be a good guitarist. Sure, there are a bunch of songs that use it, especially acoustic songs, but possessing this skill is not necessarily what separates a good guitarist from a great one :) It is, however, a very useful skill to possess. One that I still haven't learned properly.

Hope this helps. Have fun learning :)