Electric:
Hold the brush at a 45 degree angle to your gums (brush faces down toward the gums on the lower teeth and up toward the gums on the upper teeth). You should let the brush do the work. In other words you shouldn't be going back and forth vigorously with the brush. You do need to gently work your way around the front and back surfaces of each tooth and also the occlusal (chewing) surface. You should include the areas between teeth (interproximal areas) when brushing front and back. Just have the brush be in that spot and it should push the toothpaste through. A lot of the electric brushes have 2 minute timers with 30 second intervals announced so I do 30 seconds per quadrant (upper left, upper right, lower left, lower right). Don't forget the very back of the back-most teeth in your mouth. They're hard to reach and a great spot for plaque to build up.
Manual:
Modified Bass Technique. Hold the toothbrush the same way (45 degrees). Brush gently with circular motions going around the front and back surfaces of each tooth. Brush the occlusal (chewing surfaces). As you brush front and back you should be getting between the teeth in the process. Brush for 2 minutes total.