Blood transfusions are a common procedure. They are fairly standard and the follow up really depends on exactly the reason for why you had it.
Depending on why you got the transfusion, the standard blood transfusion follow up
will include: (1) questions regarding how you tolerated the transfusion. The main assessment is to ensure that you did not have an allergic reaction to the transfusion. (2) Laboratory testing. One will be to check if your hematocrit and hemoglobin increased as it was supposed to. Other laboratory testing might be done to ensure that the blood cells are ok and did not hemolyze (break down). (3) Questions regarding general health. There are rare, but possible, other complications from a transfusion. For example, rarely people get HIV or hepatitis B from the transfusion. These may take weeks to months to years to present. It is not common to test for this, but often questions will be asked.
It really does depend on why you got the transfusion. For a standard transfusion for blood loss, little follow up is needed. If you received transfusion for (for example) hemolytic anemia
-- more follow up is needed. The big question is regarding how the condition that caused your need for anemia is doing.