The actual process of terraforming starts by making machines to pump greenhouse gasses into Mars' atmosphere to trap heat. Clouds will start to form and the Martian atmosphere will slowly begin to turn from red-orange to blue with oxygen. After a while, when there is more oxygen, more astronauts will come and build cities. Even though there is more oxygen, rebreathers, which are a kind of oxygen mask, still have to worn. As it rains on Mars, bodies of water form.
Plants start to grow, and astronauts grow and harvest food.
Mars finally has enough oxygen to bring other animals to Mars. There is enough oxygen to stop wearing rebreathers.