agglutination test using blood of the donor and the recipient
Disregarding Rh factor for a moment: when you add A-antibodies to a blood sample and agglutination occurs, this means the blood contained A-antigens (A-type). The same can be said for a sample of blood to which B-antibodies are added (B-type). If agglutination for both antibodies occurs in separate assays on the same sample of blood, it means the sample contains both A and B antigens (AB-type). If the sample is said to be O-type, this means neither A or B antigen would be present in these cells. It's safe to transfuse O-type blood into any recipient due to this fact. What you also want to watch out for, is attack on the recipients RBC's by antibodies in the donor's plasma. This can result in a hemolytic transfusion reaction (HTR), but it's noted in the following text:


  Red blood cell incompatibility may also occur when the patient's RBC antigens are attacked by antibodies from the donor's plasma. This tends to be a minor problem because of the small amount of antibody present in the donated plasma, which is further diluted on transfusion into the recipient's circulation.


If you're in the lab doing a Coombs test, for example, you're checking to see if there are any extraneous antigens present that might results in a HTR. In a normal result, ergo there aren't any antibodies to RBC's in the sample mixture, you wont see any agglutination. This is for considerations outside of ABO antibodies, generally. If you're adding to B-type RBC's a plasma with known antibodies to B antigen, like O-type plasma, you can probably expect an event. To my knowledge, O-type plasma wouldn't be safe to give to anyone but an O-type recipient.

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