Do trees really get a large share of their mass from the carbon in the air?
The vast majority of a tree's carbon comes from the air, which averages 0.03-0.04% by volume (300-400 ppmv) CO2.  This is fixed through photosynthesis and eventually stored as glucose which the plant can then use for its metabolism.

Doing some quick math, this means that in order to produce 1 kilogram of carbohydrates (e.g. cellulose) a plant needs to process on the order of 2000-3000 cubic meters of air (and &approx;550 g or mL of H2O), which would fill a cube measuring 13-14 meters on a side.  Note this is an ideal figure; a plant's fixing efficiency will likely fall as it depletes the air of CO2.

Plants do take a great deal from the ground, namely water, fixed nitrogen (for proteins),  phosphorous (for nucleic acids), and several ions (sodium, potassium, calcium, among others)