To find out whether a check written to you is real or fake check the address on the check and look the address up and verify if the address is a real address or not.
Also the banks name should be on the check and you can call the bank to make sure the bank is real and ask the bank whether that check you have from the person is real or not as well.
One red flag that a check might be fake is that if there's no physical address on the check and only a persons or companies P.O. Box then the check is likely a fake check.
Real checks should have an actual physical address of the person or company who wrote you the check.