Most, but not all, furnaces have a control to force the fan to run continuously, BUT, they may not have run the wire to make it work to your thermostat. The simplest thing to do is to open up your manual and see if your furnace has a 'G' terminal. That's green, not ground, on the control panel. If it does, you'd need a cable running from the furnace to your thermostat with that wire connected. If you're lucky, there's an extra wire in your cable and your furnace has that option, and all it will take is hooking that up. For minimal control, all you need for a thermostat are two wires: R and W. When the thermostat calls for heat, it connects the red wire to the white wire. If you have a green wire, it would connect that red (power) to the green, activating the fan. The thermostat is just a fancy switch, but your furnace must have the necessary control interface to accept it.
In the absence of a green wire to force the fan on, when in Auto mode, the furnace itself turns the fan on when required.