Ok. The simplest way to learn this is to first get the antigens and the antibodies straight. Antigens are proteins on the glycocalyx...basically, they act as identity markers for a cell, telling it what comes from your body and what is a 'foreign invader.' The antigens you have determine your blood type. If you have A antigens, then you have blood type A. B has B antigens...AB has both, O has none.
Antibodies, on the other hand, are basically attack cells(the opposite of what you have.) This is because an antibody will attack a foreign red blood cell, agglutinating it and any others it can get its little hands on. i.e- if you have A blood, you have A antigens and B antibodies. If you received a blood transfusion from a person with B blood, then your antibodies, (because you have A blood, you have B antibodies) will attack and clump the B red blood cells. If you get an AB, the same thing happens because your blood will still attack the B it received. If you get an O, this blood type has no antigens of it's own to trigger your antibodies.
Long story short:
Blood Type Antigens Antibodies
A A B
B B A
AB AB -
O - AB
There is also the factor of rH, which is normally not present in a person. These usually only show up in individuals after they are exposed to it, be it either in a person receiving an rH+ transfusion, after which there body will make the antibodies against the rH, or from a pregnant mother (rH-) carrying a child who is rH+. This doesn't present a problem for the woman until her second pregnancy, in which the rH antibodies now in her blood attack the fetus. A simple rhoGAM shot will bind the the antibodies in her blood, protecting the fetus.