Crossmatching in practice
Crossmatching is performed to determine the compatibility of an individual blood donor and recipient. Unlike blood typing, which looks for specific antigens on the surface of red blood cells, crossmatching takes a specific donor patient's blood and mixes this with the recipient's blood outside of the body, to determine if a reaction will occur.
Crossmatching is performed in dogs after their first transfusion (as after an initial transfusion, antibodies form, making transfusion reactions more likely in the future), and in cats prior to their first transfusion (because cats like to be weird and have extra antigens that we can't test for, which can cause reactions - even if you've blood typed them!)
Generally in practice we would perform a major crossmatch - this is the donor red cells mixed with the recipient plasma/serum. With this we are checking the recipient doesn't have any antibodies which will destroy the donor's red cells, causing a major (acute, haemolytic) transfusion reaction.
Crossmatching can be performed using a kit, or manually. Incompatible crossmatches show evidence of red blood cell agglutination (right-hand side of the image), whereas a compatible crossmatch will show a non-agglutinated, settled 'pile' of red cells at the bottom of the centrifuge tube.