There's 3 satellites at least that you must be able to receive from of the 24-32 out there, and they each broadcast a time from a synchronized atomic clock. The differences in those times that you receive at any one time tell you how long the broadcast took to reach you, and thus where you are in relation to the satellites. So, it sort of reads from something, but it doesn't connect to that thing. Note that this doesn't tell you your orientation, many GPSes fake that (and speed) by interpolating data points.
If you don't count the cost of the receiver, it's a free service. Apparently there's higher resolution services out there that are restricted to military use. Those are likely a fixed cost for a license to decrypt the signals along with a confidentiality agreement.
Now your device may support GPS tracking, in which case it might communicate, say via GPRS, to a database which will store the location the device has found itself to be at, so that multiple devices may be tracked. That would require some kind of connection.
Maps are either stored on the device or received over a connection. Navigation is computed based on those maps' databases. These likely are a licensed item with a cost associated, though if you use a service like Google Maps they have the license with NAVTEQ and others.