The technique is pretty straightforward but perfecting can take a little time especially if you have used nothing but a guitar pick this entire time.
The right had will be the focus of this lesson. Place your right hand over the guitar strings like you would if you had a pick, but this time align your 4th finger with the high E string, the 3rd finger with the B string, the 2nd finger with the G string, and the 1st finger with the D string. The thumb will be playing either the low E string or A string.
All your fingers are responsible for picking one string except your thumb which will have to take care of two. Here is a very simple arpeggiated chord progression for practice:
One song all guitarists should know at this stage is Led Zepplin's Stairway to Heaven. You will have to google the tabs.
If you are not too serious about finger picking, you can get away with finger picking with just your thumb and index finger but you may run into problems if you want to learn hybrid picking later on.
I never went into detail about boom-chick fingering from the beginners lesson so here is a tab for the song from Buckethead's Animal Behavior starting at 2:16. You should be able to play this with what you know now.