How does Android get the coarse location? I read that Android (and similar operation systems, e.g. iOS) get the current coarse location by using either WiFi or GSM tower triangulation. I get the basic idea but have questions about the details.


Does Android normally use both methods, or does it prefer one and fall back to the other?
Does it communicate with a server to get the position via WiFi? (e.g. sending the SIDs of the WiFis to a web service)
Does it communicate with the carrier to get the position via the GSM towers or is this done on the device?
It is really up to the developer as to how to implement the location service.  The full description is available on the Android Developers official site (as captured on 24 Sep 2010)

The graph about 1/3rd down the page is pretty useful to see what a typical app might do, but again, it is completely up to the app developer.  The location service types are:


Cached Fix
Cell-ID
WiFi
GPS
Mock Location


If the app requests permission for coarse location only, it will not use the GPS to determine location.

To answer your questions:


It is up to the individual app developer, but in most cases, the sequence will be Cached Fix, Cell-ID, WiFi, GPS, in that order.
Yes, after acquiring the tower IDs or SSIDs of the WiFi signals, that data is transmitted to Google to determine a rough location.  
No, Google has done something really clever here.  Google has their own database of cell tower locations and does not require an interaction with the carrier to determine the location of the tower.


An article by Francisco Kattan on "Dynamic Cell-ID" has some of the detail. The short version is that, when you use an app like Google Maps, the app will send the current Cell-ID information back along with your current GPS fix.  In this way, Google gets a very good sampling of the signal strengths in various locations and is able to build a very rich database.