How Do Cell Phones Work?
Cell phones are designed to permit people to be moving around while using them. In order for them to be mobile, cell phones interact with cell towers and base stations. The phone coverts a person's voice into a radio frequency transmission, then sends it over the air to a nearby cell tower. The tower contacts a base station (Mobile Telephone Switching Office, or MTSO), which sends the radio transmission to the receiving phone. The receiving phone then converts the electrical radio transmission back into an audio voice transmission. As the phone moves around, the voice transmission is passed from one MTSO to another MTSO and a tower within closer range of the phone.
Technical Process
When a call is initiated, the cell phone searches for a System Identification Code (SID) on a MTSO's control channel. The control channel enables the cell phone and MTSO to communicate with each other so a call can be set-up and allow for channel changing as the phone moves around.
After the phone gets the SID, it compares that SID to the one the phone has already been assigned by the mobile phone carrier. If the two SIDs match, the phones establish a connection. The cell phone also sends off a registration request while searching for the SID.
During a call, the MTSO keeps a record of the phone's location. Once the phone starts moving out of its range, the MTSO passes the call on to another MTSO that is within range. The new MTSO then determines what frequencies are needed to continue the call.
Why No Service
Sometimes the cell phone cannot find the SIDs it needs for connecting to a MTSO's control channel. This is due to the carrier service setting up a block so they can charge what are known as roaming charges. Other times, it is because no carriers have placed any towers or base stations within a two to three square mile radius of where the phone is located, so there is no service available.

Yale University"The Physics of Cell Phones"http://www.yale.edu
Federal Communications Commission "The FCC Kids Zone - Cell Phone FAQs"http://www.fcc.gov/
Mobiledia"Mobile Telephone Switching Office (MTSO) - Cell Phone Glossary"http://www.mobiledia.com/
"How Do Cell Phones Work?." Sophisticated Edge. N.p., n.d. Web. . <http://www.sophisticatededge.com/how-do-cell-phones-work.html>.

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