I made an empty sample package with a connection manager, and a sample catalog so I could give you some screenshots.

They are attached.

EnvironmentVariable shows setting up a variable called 'ServerName' for development with the value 'Server1'. I set up a variable of the same name for production with the value 'Server2'

References shows me adding references to both environments to the project I deployed.

SettingConnectiontoUseServerName shows me setting up the relationship.

To get there, I selected the package, clicked Configure, went to the connection managers tab, clicked the '...' next to the ServerName property, selected "Use Environment Variable' from the radio group and selected it.

You can use the environments to pass values to project parameters too (I have done this for other purposes), and could use that for your connection strings if you really wanted to, but its not necessary here.

If you change your package and redeploy later, it should 'remember' your configuration and maintain it, so it will not overwrite your connections.