The illustrated heart in houndstooth was made with the pattern simply in mosaic stitch. Very simple to do by just following the chart, doing the color first and then filling in with white or a second color if you wish. I have done this one in pink and orange also, and it was stunning. Just be sure there is enough contrast in value (light and dark) to make both colors show up.
The little chart with numbers gives you the direction to take when stitching to make it easy, and also to put the least strain on the canvas and prevent warping. If you know proper basketweave, it will be super easy to understand! The same numbering sequence is also for the mosaic stitch version to make it easy.
You could, of course, follow the pattern and go straight across with the mosaic stitch rows, but this does warp the canvas a bit. ( I always stitch mosaic on the diagonal to avoid it.)
Notice on the heart that I first outlined the whole thing in tent stitch so that there would be no confusion and no ragged edges in subsequent working of the mosaic stitches that make up the pattern.
There is also another way to do the small, "woven" houndstooth - explained in the Plaid tutorial.