This seems like such a simple technique and yet I've never done it before. It's basically a garter stitch scarf, but it's made in squares. Each square is mitered by making a centered double decrease every other row creating a very distinct corner. Picking up stitches along the edge of the old and casting on the same amount plus one means that there is no need to sew all the squares together. Interestingly, I had to use garter stitch because when I made the first square and tried to use stockinette, the square turned out more like a kite. This is one place where row gauge for your scarf is actually important. The stitches need to be about square.
Size 9 needles
Various worsted weight scraps.
Cast on 31.
Odd rows: Knit 14(less one stitch every row), Double decrease, K 14(less one stitch every row)
Even rows: Knit across
You'll be taking away 2 stitches every second row and will eventually have only one stitch on the needle. Turn your work, pick up 15 along the edge of the square and cast on 16 with the next color in order to begin the next repeat.
Have fun :)