In which ways can cancer generally be found by blood testing?

Mostly it can't: 400 characters aren't enough to teach you lab medicine, but leukemias are usually (not always) found as abnormal cells on peripheral blood smear, cancers of the GI tract often present as iron deficiency anemia, and suspicion for a handful of common cancers can be increased by finding a tumor marker (i.e., alpha-fetoprotein for hepatocellular carcinoma). Labs also point up complications.