What sort of testing is done to see if a tumor is malignant?

Pathological exam. A biopsy to remove a portion or the entire tumor is performed to allow the pathologist to examine the tissue under the microscope using special stains to help assess features to make a diagnosis not only of malignancy but also the type and potential behavior of the tumor. Ancillary tests like flow cytometry, gene rearrangement test for monoclonality, presence of associated tumor markers also help.
Biopsy and pathology. The best way to determine if a tumor is malignant is a biopsy or sample, and looking at it under a microscope. A pathologist is the person trained to do this. While there are other types of tests, the best is looking through a microscope and examining the cells.