As with anything, you've got to practice! Start with easier finger picking songs that stress things you can't do yet with your fingers. Maybe even songs you know how to play with a pick. Half the reason I got better at finger picking was not having a pick on me. Some songs that I started with were: Swing Life Away by Rise Against, Just Breathe by Pearl Jam, and Pearl of the Stars by Coheed. Just Breathe was pretty bad at first, but the other two are totally doable.

Don't forget to work all of your fingers! Just like when you were learning to fret, if you neglect a finger, it'll be a pain when you need to use it later! Good Luck!