For diagnosing an engine light or other dash lights you will need a scan tool to read the code and then from there you usually go on to read live data in the relevant control module and the last step is component testing to test the suspected faulty components.
After this then repair and retest.
When reading a check engine light though you to consider that ...
Many auto parts stores will read the trouble codes for free. They use inexpensive code readers that aren't capable of reading manufacturer-specific codes. But they're free. If you want to work on your car, owning a decent quality scan tool is a very good investment.