Before I start, I fully admit that there may be faster ways to learn finger picking than this. I am not the ultimate king at guitar, but I am good at finger picking and this is how I learnt... As far as I know, there is no fast way to learn this as it is a technique that requires good finger control which is something that just comes with time. In this we are going to mainly concentrate on acoustic songs.
About 6 months into college, a film called "Old School" became popular with everyone on my music course. The part of the film that everybody referenced most was at the funeral halfway through of one of the main characters. A distraught Will Ferrel belts out Kansas's "Dust In The Wind" and everybody found it hilarious.
Its a bit daunting at first, but once you master the first part, the rest comes easily. Assuming you have enough fingers on your pick hand (you never know), put your thumb on A, first finger on D, middle finger on G, and ring finger on B. Ignore your little finger for now. You may find you struggle to stop it sticking out as though you are drinking like a dainty lady, but it doesn't matter.
Once you have worked through that you are ready to move on.
Every time you pick up your acoustic, mess around with some chords. Pick five strings at once, or try to come up with your own patterns. Improvisation is a good way to improve quickly.
I learnt another song before the next one, but it was a bit hard so I am putting one in beforehand. Blackbird by the Beatles is a fantastic song to learn, and should improve several aspects of your guitar playing. Find the tab here.
(extra homework - Yesterday)
Then you can move on to Metallica - "Nothing Else Matters".
Next is a song called "Anji" (not The Rolling Stones song). Its a folk song written by Davy Graham but the Bert Jansch version is an excellent example of finger picking. I learnt it because my dad made the deal that if I learn it, he would buy me a new guitar. I learnt it 6 years ago... still waiting.
All of this will take a long time, and probably you have skipped at least one of the songs. When you want to move on, hybrid picking is a good technique to master.
Finally, the hardest song on the list (by far). After seeing a YouTube video of this:
Amazing... its called "Jerry's Breakdown" and the tab is here
There you go - a million hours later and you can play that (hopefully). There are probably loads of other songs you could learn, but these are some of the ones that I learned that really benefited me. Hopefully this helps someone!