One way to reduce carbon output is to walk or bike to school/work. Automobiles are a big source of CO2 emissions, and they also contribute to smog. Not to mention there are other negatives as well such as traffic. So there are many good reasons to go without the car. If you cannot walk or bike, then public transportation (bus or subway) is the next best thing. A similar related idea is to use less energy at home, though this could be its own paragraph.
A second way to reduce carbon output is to offset it with planting trees. Trees absorb carbon dioxide and produce oxygen as a result. Another benefit of planting trees is that it provides habitat for animals. Many companies use a cap and trade system. This system effectively is a market where they exchange a sort of currency so that companies can produce carbon. For example, if a coal company wants to produce more CO2 output, then they would buy a credit (of sorts) from someone else to plant a tree somewhere. The tree planting balances out the carbon output.
A third way to reduce carbon output is to be consciously aware of what products you buy, and what services you use. Specifically be aware of how they produce carbon. For example, buying meat products means that there is a farmer out there somewhere who raises cattle, all of which produce greenhouse gasses. Furthermore, transporting said cattle and processing the meat also produces carbon, not to mention transporting the meat products to the store. This is just one example of how a complex chain can be hidden below the surface. Once you are aware of the carbon footprint of a product, you can be more selective in what you buy to reduce the carbon footprint.