Paper piecing involves cutting out separate pieces, most often using different types of paper, to create a bigger picture. The Scrapbooks Etc. site is one of many that have free paper piecing patterns.
I have used one of these so far in an attempt to make a handmade card and found that it worked well and looked good.
Download the pattern that you like, cut out pieces (I used an exacto-knife, but scissors work fine too).
Lightly trace the shape onto the cardstock or printed paper that you want to use and cut out the pieces. Assemble as per the finished product picture.
I have downloaded five of these so far, put them each in their own envelope, and glued a copy of the end result picture onto the front of the envelope so that finding what I need is easy later.
This couldn’t be easier.