How to Colonize an Asteroid
The best choice of asteroids for the colony will probably be a metallic (nickel/iron) object, but this will not contain many of the basic chemical building blocks of life, such as carbon, water, and oxygen in any quantity. To supply these elements and compounds, the colonists will have to locate another asteroid which does contain them and move it near the colony for processing. An alternative would be to process the material where the asteroid is found and only transport finished goods or concentrated ores to the colony.
Asteroids can be moved (especially smaller ones) through the use of chemical rocket engines, linear induction engines (mass drivers), or possibly even large (actually HUGE) solar sails.
With an abundance of solar power, it should be a fairly simple task to extract useful compounds from the carbon based asteroid.
The two most important molecules which need to be extracted from this smaller asteroid will be carbon dioxide and water. If the asteroid does not contain water, it can be manufactured from hydrogen and oxygen, which are known to be in abundance (albiet locked in other compounds) in the asteroids.