Been thru this exact headache at my old place. AC blows cold all summer, first chilly night rolls around, furnace clicks away and nothing but cold air comes out the vents. Drove me nuts for an evening untill I traced the gas line and found the shutoff handle sitting crossways to the pipe. Someone had closed it months earlier and never touched it again, since cooling doesn't need gas at all. The fix itself is simple. First, sniff around near the unit. If you smell gas at any point, stop and call your utility's emergency line, no exceptions. If it's clean, turn that handle slowly so it runs parallel with the pipe. Then set the thermostat a couple degrees above room temp and give it time. The igniter will click a few times while the air purges out of the line, sometimes for a minute or two of tries before the burner actually catches. Don't keep resetting the thermostat while you wait, just let it cycle.
Once it lights, hang around and watch the flame for a bit. It should burn steady and blue, and the blower should kick warm air shortly after. If the clicking continues with no ignition, or the flame looks lazy and yellow, that's when you stop and get a tech out instead of poking at it further.