Geodome, your example of how a racemic mixture is formed is good, but the product of your example isn't chiral, so it wouldn't be a racemic mixture.
Racemic mixtures can be formed in several ways, depending on the substrate molecule. The simplest way would be to react an achiral molecule with another achiral molecule in a way that makes a chiral carbon center somehow. A good example would be the reduction of acetophenone with sodium borohydride to form sec-phenethyl alcohol. Since the reagent can't distinguish between the two faces of the carbonyl group of acetophenone, you get a 50/50 mixture of reduction from each face. That gives you a racemic mixture.
Geodome's example is right on in that trigonal planar carbon can be attacked from either side, it just turns out that attack from either side gives the same molecule product. To have a chiral carbon you have to have four _different_ groups on the carbon.