With cold weather, chances increase that your car won't start in the morning.
If it has an ammeter gauge and the needle doesn't move over to discharge, the starter isn't drawing any current. If you have an idiot light instead of a gauge, and its light intensity stays the same, this indicates the same thing. Your battery connections are probably loose or dirty. Remove the cables, even if they're tight, and clean them. The inside of the cable clamps and the posts should be shiny. Scrape them with a knife or use a battery terminal cleaner (available for a dollar or so at auto parts outlets).
Check the cables at the other end, too. Just make sure they're tight. Sometimes the connections may loosen from vibration.
If, however, you hit the key and the ammeter needle swings all the way over to the discharge side of the gauge (the "-"), or if the warning light dims severely, you have a dead battery. That means you'll have to jump-start the car or put in a fresh battery.
What if the engine cranks but won't catch? Then you have either an ignition or a fuel problem. Check the fuel system first.
Take the top off the air cleaner and look down in the carburetor. The choke plate should be closed if you've pumped the accelerator pedal a time or two. If it's open, try to shut if by hand. Moisture may have frozen on the plate pivots. If it shuts, try to start the car. If it starts, put the air cleaner top back on and lubricate the choke plate pivots at the earliest opportunity with penetrating oil or choke cleaner spray.
If the choke plate is closed, open it with one hand. With your other hand move the gas linkage or have a friend pump the accelerator pedal. Down in the carburetor barrels past the choke plate, you should see a spurt of gas every time the throttle linkage moves. If no gas spurts out, the gas line is probablt frozen. To prevent this, use gasoline antifreeze with every tank of gas. If your gas line is frozen and you can't get your car inside a heated garage to thaw it out, you'll have to call a service station.
Of course, you may have simply flooded the engine. Push the accelerator to the floor and hold it there - don't pump it. Now crank the engine for 15 seconds or so. If that doesn't do it, check the ignition.
Remove the distributor cap and look for moisture inside. If it's wet, wipe it dry. Wipe the rotor, too. Try again.
If the cap was dry, remove a spark plug wire from a plug. Stick a screwdriver in the spark plug boot and position the screwdriver blade about an eighth of an inch away from bare metal. Have somebody crank the engine and observe. A strong blue spark should jump the gap between the screwdriver and the metal. If the spark is orange, or there's no spark at all, you've got trouble. Call a service station.
If the spark is blue, the car should start. Hold the accelerator to the floor and crank it some more.