Short answer: Normally, only the ABO group matters in transfusion. Rh type is usually irrelevant, but always considered in selection of blood.
Long answer: The only main considerations in crossmatching of blood in the normal population (that is, not a child or sickle cell patient, etc.) is that the main group and type are compatible.
The ABO group is determined by sugars attached to polysaccharide chains on the membrane of your red blood cells. Either you have one (A), the other (B), both (AB), or neither (O). Antibodies to these antigens occur naturally in the body--you never have to be exposed to A blood to have anti-A in your plasma. It forms shortly after you are born.
Rh type refers to whether or not you have the D antigen. If you do, you are Rh positive. If not, Rh negative. This antibody requires exposure to be developed, so in cases of massive transfusion, if the person does not already have anti-D, you can give Rh positive blood to an Rh negative person.
Keep in mind that there are many, many other antigens on human red blood cells. Every three days, a patient receiving blood must be screened for development of any antibodies that may have developed from the body recognizing the donor blood as "foreign".