In the double circulation system there are two routes that the blood can take:
1. Through the lungs
2. To the rest of the body
The blood starting in the heart has no oxygen in it. It flows from the heart and goes through the lungs, this is where it picks up the oxygen. The blood returns to the heart where it is redirected to go on the second route. This oxygenated blood is now delivered around the rest of the body via arteries, once the oxygen has been dropped off at the muscles (which need it for respiration) it returns to the heart deoxygenated via the veins.
Then the cycle repeats itself.