A running stitch is the stitch most people know - the basting stitch is a longer version of a running stitch. A running stitch can be used for most anything - basting stitches are really only used to keep two pieces of fabric together for fitting, applique, or machine sewing when pins would get in the way!
You'll want to start by threading your needle in one of the two ways I've taught you. Knot the thread end(s).
For the running stitch: bring your needle up through the fabric from the back (or wrong side, whichever lingo you prefer) until the knot hits the fabric. At this point, you'll simply make a stitch to the left or right of where the thread came through. Then bring the thread back up and start all over again!
For the basting stitch: simply make longer stitches, between 1/4" and 1/2" in length! These are the pink stitches in the first picture. :D
Pictures will make this easier. Follow along, now!
Keep in mind that running and basting stitches should look the same from both sides.