Best everything's random. If a point mutation occurs in a non-coding region of DNA, then it won't cause any change at all- these are called silent mutations. However, if a point mutation occurs in a coding region, then it could vary in how much it affects the protein. A substitution may have a slight effect on the protein, if it changes the amino acid to something else with slightly different properties, a massive change in the protein, such as the sickle-cell anemia case, or no change at all in teh protein, if it manages to mutate the third base in a codon, becuase there is the "wobble" which sometimes makes it code for hte same amino acid.
Over types of point mutations can do much more. Insertions or deletions of a point mutation causes a more drastic change through a frameshift. Because the amino acid sequence is read in codons of three bases, if you delete or add one base, and all the following bases are shifted a little, then every codon from that point on is completely changed. This basically makes a completely useless protein, or no protein at all.