Going downwind is great fun, but it requires different kite and board skills compared to going upwind. Many kiters initially focus on staying upwind when they start kiting. Once going upwind is mastered, going downwind opens up a new dimension in your kitesurfing. You can go on tours (downwinders) and get back into the beach quickly if you see a storm coming.
Going directly downwind is not easy as you can't edge the board to allow the kite to pull against it and generate speed. You might find on your first few attempts that you follow the kite and it loses power and falls out of the sky.
Another technique for going downwind quickly is to do giant slalom turns:
Turn from heelside to toeside then track toeside for a while
Then turn from toeside back to heelside.
Keep repeating this.
This is great practice for carving turns and riding toeside too.
When you go downwind, good board and kite speed is necessary to keep apparent wind across the kite, which generates more pull and keeps it flying and you moving.
As you bear downwind, keep edging the board a little and pull the bar in further to power the kite and keep your speed up. As you will follow the kite partially downwind the wind around you will seem to drop.
You can sine the kite (as you do in lower wind conditions) to get it to generate more power (and more apparent wind). The further downwind you bear, the more you will have to sine the kite.
You might find your kite eventually turns across the wind window to the other side. If this happens your board speed will drop and the kite will eventually lose all power and drop too. The solution it to keep it turning and bring it back across the wind window.