Pin your appliqué onto your base fabric.
Thread your needle.
Knot your thread (might seem obvious, but you wouldn't believe the amount of people I've seen forget).
Come straight up through both pieces of fabric about 1/4" in from the edge of the appliqué.
Go down at the edge of the appliqué through both pieces of fabric.
Come back up in the same place you started.
Slide your needle through the stitch you've already made in the direction you're planning on sewing. Rightys to the right, leftys to the left!
Pull the thread through the stitch.
Put your needle down about 3/8" to the right (or left, if you're going to the left) and back up under the edge of the appliqué. Make sure your needle is ABOVE the thread.
Pull it tight (but not too tight). Congrats! You're done with your first stitch!
When you get to the end of your thread, don't panic!
Put your needle through the site of your next stitch. Instead of coming back up at the edge of the appliqué, only go down.
Turn your fabric over. Get your next piece of thread ready.
Knot your next piece of thread to the one you've been using.
Rethread your needle on the new piece of thread.
Come back up at the edge of the appliqué.
Pull it through.
Do your next to last stitch as you normally would.
Slide your needle around the far side of your first stitch and put it down through the base fabric.