Removing CO2 from the atmosphere requires "sequestration." It is simple.
First, pick something that sucks CO2 out of the air and "locks it up" in its own body. Let's use trees as an example. They turn CO2 into wood, but this only works while they are growing and actually making wood. Mature trees don't sequester carbon.
Plant trees and let them grow until they don't get much bigger each year.
Cut down all the trees. Do not burn the wood nor allow it to rot. Those things return the CO2 to the air. (Heating your home with wood is no more environmentally friendly than burning coal or oil, so don't do that.) Use the wood to build houses, furniture and stuff, or bury it really deep where it cannot get any oxygen. Wetlands work really well if you can get the trees to sink into the mud. They quickly run out of oxygen in the mud and won't rot. Expect to encounter some resistance when you announce your plan to use wetlands as a landfill because not everyone is eager to sequester carbon. If you bury the wood deep enough and wait long enough, it turns into coal. Don't burn it, either.
If you need more room for more trees, you can convert farmland to forest, but then there will be less food and food will cost more. You can also cut down old forests. They aren't useful to sequester carbon because the trees are not growing or they grow very slowly and so they don't turn very much CO2 into wood. You will gain the most efficiency by targeting the oldest and biggest trees. Do expect some resistance at this point. When you start chopping down mature forests like the California Redwoods or the Michigan White Pines you will learn that not everyone is eager to sequester carbon.
Left to its own, nature is very inefficient at sequestering carbon. A rain forest, for example is a total waste of space. The plants and trees are allowed to rot and release all the carbon back into the atmosphere. If you hope to get any carbon sequestration efficiency out of the rainforest, cut down the trees and use them to make tables and lamps and stuff. Expect to meet resistance at this point when people learn that you want to cut down more rainforest and sell off the lumber. Again, you will learn that not everyone is eager to sequester carbon.
That's about all there is to it. Cut down all of the biggest trees you can find, use them to fill in wetlands or bury them really deep and plant little trees.