Debbie's good writeup above can be simplified in terms of the presence of absence of H substance. If we let capital H represent the normal gene for H substance and little h represent the abnormal gene, then a person can be either hh or non hh (either HH or Hh).
hh is homozygous absence of the gene for H substance -- if you have this you would not produce any H substance - and have the ridiculously rare "Bombay phenotype"
If a person is hh, then his/her blood group is Oh, regardless on what his/her genotype for A or B. If the person is not hh, his/her blood group will depend on the ABO system.
The Bombay phenotype is thankfully rare as anyone with it can be almost assured that it would be supremely difficult finding blood for them if they required a blood transfusion.
Source: Harrison's online.