I know this doesn't relate to the reassembly process, that's been covered in the other answer by Paul. However most of the time, the rear sprocket is not physically attached to the wheel. They are two separate pieces which have rubber inserts between the metal "teeth". The rubber inserts are there for dampening torque from the motor if you let the clutch out too fast or drop the throttle quickly. If the sprocket were bolted directly to the wheel, anytime you applied or removed power, the difference in torque load being applied could be great enough to cause the tire to break free from the the riding surface unexpectedly, which depending in when it happens, could be catastrophic.
As long as those rubber inserts are still pliable and not degrading, they should be fine. They are a consumable part and relatively inexpensive to replace. You will get a smoother power delivery to the rear wheel with new inserts if the old ones are getting hard.
I am more concerned about the condition of your rear sprocket. The valleys between the teeth should be circular and the angles of the side of the teeth should be the same on both sides. Based on the picture you posted, your sprocket looks rather worn; I would recommend replacing the front and rear sprockets and the chain. Here's what a new front/rear sprocket should look like: