The basic terminals on a thermostat are R G Y and W. The wiring should be color coded R for red, G for green Y for yellow and W for white.

R is the terminal coming from the transformer that is powered all the time. The thermostat is actually a group of switches designed to energize different circuits. R is the main power source. The G terminal receives power from R and energizes the fan circuit when the fan switch is turned on. When the fan switch is in the automatic position G is connected to the Y terminal. Y is the terminal that is used to turn on the cooling circuit. The Y terminal is connected to the R terminal when the Heat/ Off / Cool switch is in the cool position and the temperature has risen above set point. This energizes the cooling circuit and the fan circuit.

The W terminal is used to energize the heating circuit. When the Heat/ Off/ Cool switch is in the heat position and the temperature has dropped below setpoint R terminal is connected to the W terminal and the heating circuit is energized. On a typical gas furnace the fan is energized from a temperature switch that senses the temperature of the heat exchanger or a timing mechanism in a circuit board that senses power on the W terminal.

Some thermostats have other terminals. The most common are RC and RH which are used if you have a system with seperate 24 volt power supplies for heating and cooling. If you have 1 power supply the RC and RH must be jumpered together. Another teminal is C. It is used to connect the other terminal on the transformer if this particular thermostat requires a common wire for operation. One other common terminal is O or B and is used to power the reversing valve for a heat pump. If you are using O or B you will most likely also have a terminal labeled W2. This terminal is used to energize the backup heating system for a heat pump and energizes  if the building temperature falls to far below setpoint.