Thermostat wiring can be intimidating, but it is fortunately more intuitive than most types of wiring. Newer thermostats have a fan "Auto/On" switch, which enables independent fan control. This means that the fan can operate without the heat or air conditioning running. When replacing an older thermostat, you will find some standard wiring.
The red or yellow wire operates the air conditioning. The green wire is the fan wire and allows for independent fan control. Your white wire is your heat. To wire your thermostat for the independent furnace blower fan, simply ensure that the green wire is connected to "G." Once this is done, all that is left is double-checking the other wires to make sure they are plugged into their appropriate spots.
Note that electronic thermostats operate slightly differently, insomuch that they use a resistor. This difference will be evident by the presence of the "C" or common wire. Furthermore, you may find that you have more than one transformer, in which case you will see 2 red wires, one for each transformer. One may be designated "RH" for red heating, while the other would be "RC" for red cooling. These wires do not affect independent fan control.
If your fan is in the "Auto" mode, you will likely find that the "G" and "Y" will be connected at all times. To allow independent fan control, be sure to separate this connection.