How much is my baby able to see?

More than you think. Babies are generally credited with clear vision out to 12-15 inches but it gets fuzzy further out. They are nearsighted because the eye is small but it grows and kids should be at their best vision by 5 or so (20/20) . They are fascinated by lights and bright colors and can often mimic some of your facial expressions and tongue movements within the first few months.
More than you think. A baby, at birth, show a preference for looking at faces, and can see your face when you hold him/her in your arms. Visual acuity and focusing ability improve quickly in the first six months of life. Babies do see color, and seem to be attracted to patterns of light and dark.