How are carbon dioxide and oxygen carried around your body?

By the Blood Stream.

Arterial Blood, is the oxygen carrier.

Venal Blood is the Carbon Dioxide carrier.

Oxygen is absorbed into the blood stream in the lungs. It is then pumped around the body, by the heart, through the arteries (Arterial Blood). At the point of use , muscles etc, it is converted into carbon dioxide.

The carbon dioxide is pumped back to the lungs by the heart through the veins, as venal blood. whereupon it is released into the the lungs to be exhaled.

The whole system is done in TWO(2) parts. and theheart has four chambers to keep the different bloods separate.