The early folk guitars players were strummers.  They would use a pick or their thumb and strum all or most of the strings at the same time to create chords.  Then Merle Travis came along and popularized a type of playing called fingerpicking or, after Merle, Travis picking.  With Travis picking, each string is plucked individually with the thumb and fingers of the right hand (usually with the thumb playing an alternating bass line) while the left hand forms the chord to create a somewhat more fluid sound.  The style was made even more popular by Chet Atkins.  If you like Dust in the Wind by Kansas, you like Travis picking.

Here are some items to get you started:

A Book

Most guitar players and teachers agree that the best book to start
with is Contemporary Travis Picking by Mark Hanson.  The book starts
you out with simple patterns and gradually gets into more complicated
stuff.  It also comes with a CD so you can hear how you are doing.

Two Good Songs to Start With - Dust in the Wind and Landslide

I’d start with Dust in the Wind by Kansas and Landslide by Fleetwood Mac.  Both songs use a very
straightforward Travis picking style and the chords are relatively easy
to play.  It is also easily recognizable by others - making it a pretty
fun one to start playing when somebody hands you a guitar at a party. Clips for both songs are below.

Sheet Music

And here are links to sheet music for Dust in the Wind and Landslide from Sheet Music Direct.

Video

And when you are ready to see Travis picking combined with all-time great hair and tuxedo fashion, click here.