The process of deleting a database varies depending on the database management system you are using.
SQL Server
You should use the tools supplied with SQL Server to delete a database. Speak to the administrator of your SQL Server database.
Oracle
You will have to use the tools supplied with Oracle to delete a database. Speak to the administrator of your Oracle database server.
Cloud
A database can be deleted, however, it cannot be the database that is currently open. This is to reduce the chance of a database being accidentally deleted.
If you do not want to delete a whole database but only some items from it, there is an option for deleting database objects. These objects will remain in the Recycle Bin until you empty the bin or restore the items.
Other database management systems
You would typically use standard Windows procedures to delete a database file.