How do I check the codes of an SQL database?

You can connect to the database server instance using a client tool like Toad for example. Then you will be able to see the databases hosted in the instance and all the objects within it like tables, procedures, functions etc.

The type of client tool you use will depend on what RDBMS product you’re using. Toad can be used for Oracle, MySQL, MS SQLServer etc. MS SQL Server also have its own client tools like SQL Server Management Studio and SQL Operations Studio which comes as a free installation. MySQL also has workbench