How does a true airspeed indicator work?
For a basic True Airspeed Indicator (TAS Meter) like the one shown below, you simply dial your pressure altitude into the top window using the knob (aligning it with the appropriate temperature mark at the bottom of that window), and then read your true airspeed in the other window at the bottom.  



Your pressure altitude can be obtained by setting your altimeter to 29.92 and reading the indication, the air temperature can be obtained from an outside air temperature (OAT) gauge (or you can use one from the Winds Aloft forecast if your aircraft does not have an OAT gauge), and the combination of the two gives you your density altitude.
The meter itself is simply a mechanical slide rule, performing the same functions as you could do manually on an E6B flight computer.

The indicator above is showing a true airspeed of about 202 MPH, at a pressure altitude of 10,000 feet and a temperature of -15 degrees.



For a nice video tutorial check out this one from the University of Oklahoma.