Below I've 'drawn' a step by step visual (hopefully) of how I do my appliqué. I'm not a brilliant drawer but I hope it is clear enough for you to understand. There is a legend of what is what at the top of the drawing showing what the colours, of pens I used, represent.
The thread I like to use is YLI silk thread but I also like YLI soft touch which is a fine cotton thread (also good for piecing). Use a colour to match your appliqué. (however with the silk there's a lot of lee way).
I like to use a quilting 'between' needle usually in a size 10 but I'm currently practicing with a straw needle. (the jury is still out on this one) I don't like the appliqué needle but you find your own preference. Just bear in mind it should be a fine needle.
Make a small quilters' knot in your thread. Come straight up from underneath the background into the fold of the appliqué piece catching a couple of threads of the fabric. Then take the needle back down into the background in the same spot that it came out of. The needle then travels in a straight line under the background fabric to where you will make your next stitch into the appliqué in the same way you made the first one. Straight up. You should aim to make the distance between each stitch even and as small as you can ie between 1/16th and 1/8th, ensuring it is smaller around curves and on inner points particularly. At the end of your appliqué continue a few stitches past the beginning again and then with your needle through to the back make a couple of backstitches into the background only.
My favourite method of appliqué is usually with freezer paper underneath the appliqué. It can be removed in two ways. Either commence you appliqué on a straight part and at the end leave little gap to remove paper (tweezers are a great help here) before finishing. OR make a little slit in the background and remove paper that way. Generally though, for ease of quilting it's best to cut away the back ground but sometimes with tiny skinny pieces this is not advisable. Use your own judgement. I hope I have helped some of you new to this techniqué. These are basic instructions to show the appliqué stitch to get you going. I'll try post other tips over time.
Click on the picture to enlarge.