Hi bobbiekay and dancysko,
As acicomp has mentioned this is a very open ended question. Telecommunications can be a technically complicated environment.
For a very brief outline from my understanding:
There are 3 main technical layers involved in a Telecommunications network. The Radio Layer, The core Layer and the billing layer.
The radio layer is basically, as the name suggests, the radio waves that are beamed out from a basestation tower, and picked up by your cell phone. These radio waves are generally broadcast across a certain frequency or spectrum, which your phone is also tuned to. Mobile operators pay large sums of money to governments bodies in order to access these spectrum ranges.
The Core layer consists of a series of "servers" which perform specific functions for you when you make a call. Two core components are:
Switchs - These handles the routing of calls from point a to point b.
HLR - This holds specific service information for each customer. For example if I have initiated call forwarding on my phone, this instruction to perform call forwarding when I receive a call is stored in the HLR. It also stores you current location on the radio network, so that the switch knows where to route an incoming call.
The Core network is by far the most complex layer of a telecommunications network, and as services become more complex, such as 3G capability, so do the components of the Core Layer.
Finally the billing layer. This is where your calls are timed, charged and/or billed for. For contract services you have call detail records created for each call you make. Within these call detail records you have all the different charging elements of the call. For example if the call was an international call, the duration of the call, peak or off peak times. These is all stored centrally in a database until it is time for your carrier to bill you for a months usage, whereby your calls are calculated and summed and a bill is generated. In the case of prepaid services the billing occurs in real time and an account balanced is checked before a call is connected and then debited as the call is being made.
A very basic overview, but if you would like more info you could try:
http://www.mobilein.com/mobile_in_a_minute.htm
Or try a search in wikipedia.
Hope that helps a little
Cheers
H