The mildest geoengineering strategies are to pull harmful gases from our air, particularly carbon dioxide and methane. Carbon dioxide comes from burning fossil fuels and is the worst contributor to climate change. Methane is stronger, but it breaks down more quickly in the atmosphere. Thus, many scientists are concentrating on C02.
Yet C02 can be filtered naturally from the atmosphere in ways that we're already familiar with: planting trees. It's a simple method to remove C02 from the air because trees naturally absorb it. It seems like a no-brainer at first, but there are still complications. It needs to be performed on a large scale (think forest-sized swaths of foliage), and trees take a long time to grow. Some scientists are also concerned that new forests could take up valuable land needed for farming.
Still, of all the geoengineering schemes on the table, this is the easiest and most affordable, and has the fewest negative consequences. It won't solve our problems, but it won't hurt, either.