Look closely at PDFs
Not all test centers support the digital certificate and issue the test result as a PDF file instead. However, these are particularly easy to forge. Since most PDF certificates are sent by e-mail, you can at least ask the person being checked to also show the original e-mail with which the certificate was sent.
With a PDF, one should always pay attention to the date and time of the sample collection. If the font is different or if it is too small / too large, this can be an indication of manipulation. Then one should become suspicious. For example, you can google the test site. Maybe it is a certificate of a test center that no longer exists. After all, many service providers have discontinued their offers in the meantime.
Handwritten certificates are probably the hardest to spot as fakes. Nevertheless, to be on the safe side, you can also Google the issuing test center in this case to check whether it actually exists.
Checking digital test certificates via app
Digital test certificates can usually be checked using the CovPassCheck app. After scanning, this shows the time when the sample was taken. This prevents the use of old or forged certificates. It is also possible to check the validity of test certificates within the CovPass and Corona warning app by clicking on the respective certificate and checking the information.