Check for voltage drops all along the circuit. Get a good wiring diagram for your car. For older cars that are common, I think Motors have wiring manuals. If your old car is a 1952 Ferrari type of which only less than 10 were built, good luck! Most of the common American car post WW2 will have manuals available. When trouble shooting always start with the battery, unless it is a charging problem in which case start with the generator or alternator if it is newer or has had a conversion.
Your wiring diagram is like a road map. Your trip starts at the battery, goes through a switch of some sort, and then through what ever components it needs to the component it is controlling, and then to ground.
Take an example, your lights don’t come on when you turn on the light switch. Start at the battery, Do you have good voltage with everything off? 12-13 volts on a 12 volt system. 6-6.5 volts on a 6 volt system. Turn you ligth switch on, check you voltage at the battery again. Did it drop? If your voltage was slightly above 12 volts or 6 volts and it dropped to 12 volts or 6 volts +/- .5, the battery is good. If it dropped 2 volts or more, the battery has a bad cell, and needs replaced.
The battery is good, but the lights still don’t come on. Do any lights come on? More importantly what lights don’t come on? If everything comes on except one headlight or one tail light, look for a bad bulb. Tail light bulbs are pretty easy to check by taking them out and looking. Sealed beam head lights are more difficult to tell. If it is a headlight on an older car with single headlights, use your dimmer switch to go from high beam to low beam. If the high beam comes on, but the low beam doesn’t you need a new headlight.
If both headlights don’t come on, you probably have another problem, unless you have been driving for a while with only one head light and then that also quit! If that is the case, you need to improve your vehicle maintenance
Lest stay with headligths for our example and lets say you have a 1955 Studie like Kristin. You will have a ligth switch mounted in the dash, a fuse for lights in the fuse block, and a dimmer switch on the floor. Check your fuses. Older cars will have the glass “tube” style fuses. When one blows, it is obvious. If you find a fuse blown, good luck. You are going to need to work a little. Fuses don’t typically blow without a cause, usually a short. Did you have a “little” fender bender recently? Look to make sure that your wiring to your headlights did not get damaged. If you find a place on the wire where it chafed on a damaged fender, Use your electrical tape to fix it temporarily to get home, and fix it correctly the next morning. That may involve putting in a new wire and knocking the fender out a little so it does not chafe the wire until you can replace or repair the fender. Replacing blown fuses never fixes a problem, and putting in a larger fuse or a heavy gauge wire instead of the fuse is a great way to start a fire!!
Fuses are ok, now check voltage at the fuse. Is it full voltage? Good. If it drops significantly either coming in or going out of the fuse, you have a dirty connection right at the fuse block. Clean it.
Ok your fuse and fuse block were good. You have good voltage going out of the fuse block to your headlights. In our example of the 1955 Studie, you have a dash mounted headlight switch, and a floor mounted dimmer switch. They will be mounted in series with each other. Series means that power goes to one switch, out that switch and to the other switch before it goes to the headlights. Normally it would go first to the dash switch, and then to the dimmer switch before going to the headlights. do you have voltage to the dash switch? If not you have a broken or corroded wire between the fuse block and the dash switch. If you have voltage into the switch, do you have a voltage drop going out? A large voltage drop or no voltage going out means you need a new switch. If you light switch checks out, check the dimmer switch the same way. If you have good voltage out of the light switch, but low voltage to the dimmer switch, you have a problem with the wire running from the light switch to the dimmer switch.
This comment has gotten kind of long, but I’m trying to show that you need a logical step by step trouble shooting process to find find and fix electrical problems. Just think of your wires as a road for electricity to travel on, and your wiring diagram is the map. I have seen guys just start throwing parts at a problem. That is an expensive way to fix your car! Auto parts stores will not usually take electrical part back once you walk out of the store, so you can end up with your own auto parts store in your garage if you are a parts changer.
A couple of quick tips before I close this comment. If one or more headlights have a dim yellow glow instead of shining brightly like they should, look for a bad ground. If your dash lights go out at night, you have probably blown your taillight fuse. Auto manufacturers typically put the tail lights and dash lights on the same fuse circuit so that you will know when your tail lights quit working. That is because, if you don’t walk around and check your lights before driving, you won’t know if your tail lights are out.