Three hand stitches will get you through just about any basic task -- the slip stitch, the backstitch, and the running stitch. Start by threading a needle with a 24-inch length of thread. Knot just one end; it's unnecessary to sew with a double thickness of thread.
Use this stitch for hemming. It is virtually invisible and very durable -- the thread is hidden inside the fold of the fabric, where it's not subject to wear and tear. Make a small fold in the fabric, just enough to encase the raw fabric edge; press the fold. Then make another fold the size you want the hem to be. Put the needle inside the fold, push it through to the front layer of fabric, and pick up just a thread or two of the fabric. Send the needle back into the fold, and repeat.
Approximates the straight stitch on the sewing machine. It is strong, perfect for mending a seam. With right (front) sides of the fabric together, bring the needle through the two layers of fabric. Insert the needle back down through the fabric about 1/8 inch to the right; bring it back up 1/8 inch to the left of where you started (so each stitch will overlap the last by 1/8 inch). Repeat.
Also called basting, this joins pieces of fabric together temporarily. Novices may want to baste before sewing. Insert the needle at evenly spaced intervals into the fabric several times, then pull needle and thread through. Repeat.
After hand stitching, the thread has to be tied off: Take a tiny stitch on the wrong (back) side of the fabric; before pulling the thread all the way through, send the needle through the loop of thread. Pull the thread until a second small loop forms, send the needle through that loop, then pull taut.