What blood tests would be done to check for a b12 deficiency?

Can be as simple: As just testing a serum/blood level of vitamin B12. There are other tests, like a serum homocysteine or methylmalonic acid level that can better deteremine deficiency when serum levels of vit B12 are borderline.

B12 level: It is quite easy to check a B12 / folate (folic acid) and if necessary a methylmalonic acid level. VIt B12 deficiency may cause a mild anemia with large red cells (megaloblastic anemia). It would be typical to check a blood count with the B12 levels.