Since we lit our pilot light within the last 30 minutes, we turned on the heat, however we CANNOT turn off the fan. Whenever we try to cut off the heat, it just blows cool air. What is wrong? 
Two possibilities that come to mind are:
Someone bumped the “FAN ON/AUTO” switch on the thermostat to “ON” making it stay on.
or
The blower/limit switch is stuck. This is a heat-sensing switch assembly in the heat exchanger part of the furnace (somewhere around a foot above the gas burner) that turns on the blower once the furnace is hot (in order to not blow cold air for the first minute) and if the furnace gets too hot (in case of blower failure, etc) it cuts the gas. They’re fairly generic and easy to install, but you may want to defer this to a furnace repair company as they’ll have the thing on hand and know right where it is in your furnace.