Carbon sequestration is an excessively expensive and probably technically impossible method of capturing significant amounts of carbon. Planting trees is another popular suggestion for sequestering carbon, but a more traditional method has not been mentioned to the best of my knowledge.
Building up the soil is a simple low-tech technique for sequestering carbon. For centuries, careful farmers have realized how to build up the fertility of the soil, not really thinking in terms of carbon sequestration.
Commercial US agriculture is largely based on "robbery agriculture," as the great German chemist of the century and a half ago, Justus von Liebig, put it. When I published my book, Farming for Profit and a Hungry World, 30 years ago, I discovered that US agriculture was eroding about 30 pounds of soil for every pound of food it delivered to an US table. At the same time, my research for the book found that US agriculture was burning about 10 calories of fuel for every calorie of food that it was delivering to a US table.
I have no reason to believe that these imbalances have gotten any better since then. I strongly suspect that they have gotten worse.
So, the plan for reducing carbon by way of agriculture is to grow corn, perhaps the most industrialized crop, in order to produce ethanol. This process produces more energy than it consumes, only if a lot of credit is given to the energy value of the residues, which are fed to cattle. Even then, the net gain in energy is minimal and ignores the intensive consumption of water and the carbon released from the soil.
Yet, careful agriculture, by putting more organic matter back into the soil, builds up fertility, while sequestering carbon. This kind of traditional agriculture uses less mechanization.
Does this technology mean that society must revert to turn more people into downtrodden farmworkers? Capitalism might impose such an imperative, but the technology certainly does not. After all, many Sunday newspapers have a special section devoted to gardening because people find that sort of activity pleasant.
Final caveat: I do not pretend to have developed detailed data on how much a rational and cultural system could contribute slowing down global warming, but I do know that the direction we are heading is wrong.