For a while now ArcGIS Desktop has had a cosy relationship with ArcGIS Online and it all started like an arranged marriage configured by default via your GIS Administrator.
However this relationship will only work if you have an internet connection (to http://www.arcgis.com) , if not and you have a local Portal for ArcGIS server then you can Add a different portal URL and continue in a more secretive place.
So you can see if there is a relationship when you start ArcGIS Desktop which puts a globe icon in the system tray so you can see at a glance what the connection is like.
If you do not sign in you can only see Public content from Desktop, which may not be what you want. Otherwise you will need to be a named user which you may be entitled to. A named user (typically with a username and password) can be associated with just a single Organisation, the site administrator for your organisation or portal looks after the way you become a named user.
Next from Desktop we need to sign in, unless you have earlier opted to sign in automatically.
And now enter your username and password.
Once you are connected and signed in as a named user, you may be able to join and participate in group (any number of which you could belong to) activity out of the gaze of the public, like being able to contribute.
Now we are ready to start taking a look at what this relationship with your collaborative GIS content management system called ArcGIS Online (or Portal for ArcGIS) can offer you via Desktop.
But the good stuff will have to wait until Part 2, promise to leave anything that is not Free or Easy until the end.