How do I get the total number of databases that are active?
In singletenant (non-CDB, old) architecture: one instance - one database. In multitenant architecture (CDB): one instance - multiple databases. 

So first of of you have to know the relationship between instance and database. Then you can identify how many instances do you have on your server (how, it depends on your operating system) and then you have to identify what architecture do you have (non-CDB, CDB). 

Than you can make a list of all databases. Take a look at https://stackoverflow.com/questions/36957919/how-to-list-down-the-list-of-pdb-and-cdb-in-oracle-12c

Edit:
As mentioned by jmk, you can meet also Oracle RAC.