Today, we transfer our blood easily as we know our blood group.
But what did people do before that discovery (in 1901 by Karl Landsteiner, then independently in 1906 by Jan Jansky and 1910 by William L. Moss) when it came to blood transfusions?
Short: before the knowledge of blood typing transfusions were attempted and near all failed.
Long: There were many attempted transfusions that were mostly fatal. The first attempted (recorded) transfusions were practise by the Incas. Since 1616 when circulation was first detailed practitioners have been attempting to transfusion substances. These include beer urine and animal blood among many others. In the 1800's there were a few successful blood transfusions but fatalities occurred so this research was shut down until Karl discovered blood types. And the first successful transfusion using his know edge was completed in 1907. Blood borne diseases were still pretty much unknown.
The first recorded blood transfusion was done on dogs in 1665. Two years later, blood was successfully transferred from a sheep to a human. In 1818, James Blundell, an obstetrician, successfully treated a patient with postpartum hemorrhage with her husband's blood.
The main problem that stood in the way of the development of blood transfusion was the tendency for the blood to clot and to block the tubes or apparatus connected to the recipient. In 1873, Sir Thomas Smith of St Bartholomew's Hospital, London, is reported to have successfully transfused blood from which the clot had been removed (ie defibrinated blood). Attempts by Dr James Braxton-Hicks at Guy’s Hospital in 1883–84 to overcome this problem using sodium phosphate mixed with the blood as an anticoagulant resulted in the deaths of the patients
About half of the patients died:
But in 1873, F. Gesellius, a Polish doctor, slowed the transfusion revival with a frightening discovery: More than half the transfusions performed had ended in death. Upon learning this, eminent physicians began denouncing the procedure. The popularity of transfusions once again waned.
Franz Gesellius favored transfusions from animals over transfusions from human to human. But instead, milk and saline transfusions gained in popularity through this discovery.
Even after the discovery of blood groups, it took years until first testing whether the donor and recipient blood matched became standard practice. Until then, transfusions were usually "direct" - from one person's vein directly to the recipient.
Pretransfusion testing did not become normal practice until indirect transfusion became popularised by the use of sodium citrate anticoagulation and collection of donor blood, which occurred after 1915.
A brief history of blood transfusions (includes references to the first successful blood transfusions)