What connection string to use for Azure SQL DB using Active Geo Replication?
You can now create a failover group and set up auto-failover (currently in preview) and then you will have a read/write listener connection string
Go to the Azure SQL Server (not a specific database) -> Failover Groups -> Create and fill in the required info - servers, DBs and policy 
After the group is created you will have a listener connection string you can use across both DBs in the failover group configuration details
For more info, please check https://docs.microsoft.com/en-us/azure/sql-database/sql-database-geo-replication-overview#auto-failover-group-capabilities
Your application has to connect in the same way to the readable secondaries as you did from SSMS: You have to use the connection string of the server that holds to replica.
Failovers can be triggered use T-SQL commands, PowerShell and through the management portal. Check these two documentation articles:
Active Geo-Replication for Azure SQL DatabaseTerminate a Continuous Copy Relationship