It's a good idea to have a few sample or pratice pieces on hand before actually doing it on your beautiful project.
Zig is the stitch made with the needle down in your background fabric
Zag is the stitch made with the needle down in your applique
You want to always start with the needle down into your background right next to as close as you can to the edge of the applique and you want to pull your bobbin thread to the top of your work and hold those threads in your left hand and begin to stitch, Now it only makes sense that when you think about it when you zig zag your needle moves side to side or right to left, so you have to make little adjustments with your project by pivoting your work especially for curves and points. Just before you reach the point say on a leaf applique you want to stop with the needle down in your applique(zag) just one stitch away from the point. Now make your adjustment by turning your work so that when you begin to stitch again your zig is going to land right on the point of your leaf.
Resource:Simply Successful Applique by Jeanne Sullivan, comes with a CD full of step by step instructions and wonderful step by step photos, for every kind of applique hand and machine.