There's a lot of variations in railroad signalling. Track circuits are really, really popular, though, because they provide both block occupancy detection and broken rail detection, quite cheaply.
When the signalling is down, communication is done by radio. (Actually, communication is *always* done by radio; this is semi-redundant with the signalling where there is signalling.)
In so-called "dark territory", the dispatcher must keep track of where the trains are manually, and issue movement authorizations to each train by radio. In the old days, this sort of order was communicated by telegraph, printed on paper, and handed to the conductors at stations, but since radio was developed, they're generally communicated over the radio.
There are a number of different methods of operation (procedures). "Timetable & train order" was an old one used in the US (and practically nowhere else) prior to radio and prior to good telegraph service. Almost everyone worldwide (including the US) uses some variant of block occupancy rules now. The basic principle behind "block occupancy" rules is that each train has authorization (from the dispatcher & signal system) to be in particular blocks of track, and must stop if they are in danger of entering another block without authorization. There are various methods used to make sure that you never authorize two trains to enter the same block at the same time, and that you never authorize a work crew to be in the block at the same time as a train, and so on...
Speaking of broken rail detection, there was one very infamous sabotage incident on the Sunset Limited in 1995 where the rails were detached from the ties (in order to cause a derailment)... and the saboteurs deliberately connected wires across the ends to make sure that the track circuit didn't register that the rails were broken....
http://www.ble-t.org/pr/news/headline.asp?id=14688