How do you know if you are genetically predisposed to a mental illness like schizophrenia?

Family history. If you have any blood relatives (e.g. Siblings, parents, uncles, aunts, grandparents) with schizophrenia, then you are at increased risk of developing the disease yourself due to genetic factors. The more relatives that have schizophrenia, the higher your risk. However, most individuals who develop schizophrenia have no family history of schizophrenia, and such cases seem to arise "de novo.".
Ask you family. You are genetically predisposed if there is a family history in genetically related relatives (blood relatives). But, this does not mean you will get a mental illness. It just means you are at a slightly higher risk than someone without a family history.