You have most energy in the beginning when you start brushing your teeth therefore it is best to start with the areas that is most difficult to brush. Like the teeth furthest back in your mouth, such as your wisdom- and back teeth.
The inside of the front-teeth in the top and the bottom of the jaw should be brushed with the toothbrush straight out. Make sure the bristles touches the edge of the gum.
Make sure the bristles of the toothbrush also touches the edge of the gum while you brushing the inside, the outside and the chewing surface of your teeth. (Most bacterias collect between the teeth and around the gum-edge)
Brush your tongue from back to front. Brushing your tongue helps remove plaque, which can cause bad breath and help bacteria grow.