Graph paper, but you can use Word, and I've seen articles about other software like Gimp, which is open source and free.
Inkscape is a vector program and free.

About Paper Piecing | Sewhooked
At the bottom of the page there are links to Gimp and Inkscape
Link to Libre Office which is an open source office app like MS Word. There are tutorials for Word.

This link also mentions an app for the iPad. (not free)