1) Carbon is removed from the air by photosynthesis in plants
2) Feeding, from animals, passes carbon along food chain/web
3) Carbon dioxide is released back into the air by:
-animals & plants respiring
-bacteria/fungi acting as decomposers
-Burning of fossil fuels (combustion)
Pic at the top is from my old biology book, incase u don't understand it still.
Hope I helped :)