there's 3 factors that lead to a breathable atmosphere
-Breathable gas (oxygen for the most part) must be within a certain range, determined by race
-Pressure must be within a certain range, determined by race
-There cannot be ANY dangerous gases
The easiest way to create a breathable atmosphere on a body with no atmosphere is to manufacture Oxygen until you reach the minimum requirement. For Humans, in version 6 and above, it's 0.1 atmosphere. Then switch to creating Nitrogen (say 0.3atm) Eventually you will be alerted that a breathable atmosphere has been created.
The fly in this ointment is temperature. Even with a breathable atmosphere, many worlds will be too warm or too cold to be fully habitable. Humans in version 6 have an ideal temperature of 14C with a deviation of 24C, meaning they can comfortably inhabit worlds with 'surface temperatures' ranging from -10C to 48C. The thickness of atmosphere and the presence of greenhouse gases can raise the temperature of a planet. Anti greenhouse gases can lower it. The Moon has a base surface temperature of -53C, which is fairly easy to deal with. After you have a breathable atmosphere you can simply add a greenhouse gas until the temperature reaches a comfortable range.
Mercury is only slightly more difficult. Mercury has a base temperature of 427C. Which is a lot, but the anti-greenhouse effect is actually really powerful. I tested in SM mode and you can get a safe temperature on mercury with about .7atm of Anti-Greenhouse Gas, 0.1 oxy and 0.3 nitro.
Airless worlds are usually only difficult if they are far from the sun. It takes a lot of greenhouse effect to make frozen rocks habitable. Worlds like Venus, with high existing atmospheric pressures are also nearly impossible to colonize. Reducing the atmosphere to useable levels would take several decades for all but the most enormous terraforming project.