The method of terraforming I'm thinking of is hauling the minimum required load of compost to the world to be terraformed, dump it on the planet's surface and seed it with plants that are hardy in an oxygen-poor atmosphere. Then, the plants convert CO2 to O2 and sugar which they use to grow, resulting in more compost on every iteration of the cycle of life. Like desertification but backwards. Follow-up passes by the terraforming crew will seed the world with less hardy plants.
Now, what I'm wondering is this: can this process create a habitable zone on a planet, at least on warm-enough latitudes while the terraformed area expands mostly on it's own? In particular, I'm thinking of a frontier world with mostly animal transport where a homestead will have an emergency cabinet with oxygen masks for the family. As for livestock, stall- to barn-sized oxygen tents, or caulking and crossed fingers, and maybe a second-hand oxygen regulator, for those without.