Troubleshooting electrical problems
Most electrical problems are due to poor connections. Batteries and alternators will go bad in time and should be tested at your local parts store IF the basics mentioned here do not fix the problem. Take both in at once to eliminate further problems.
 Cleaning terminals
Start at the battery. Regardless of how the connections look, remove the cables. Remove the positive cable first, then the negative cable. Use a battery terminal wire brush tool to clean the battery terminals and the cable terminals. Remove all old oxidized contaminants. Be aware that lead is likely present, so wear gloves if you are concerned about lead migrating through your skin.
To prevent future corrosion, a light coating of non-conducting grease such as Dow Corning DC4 should be applied. While a professional might not recommend this, I had Japanese mechanics put regular bearing grease on my car battery terminals when I was overseas and it never presented a problem. It seemed to prevent acid build up and corrosion.
Remove the other end of the battery cables and clean those terminals and where they mount with a wire brush. Make sure you see shiny bare metal. Again a light coating of non-conducting grease would be optimal, but not mandatory.
 Battery terminals
A much better option is to use one of the collet type terminals like is now sold by Accel, shown below. They have a much better retention method than the type shown above.
Another option is to use an eye terminal sized to the cable, attached to a marine type terminal that has a lug and nut to hold the eye terminal in place.
The battery negative (-) terminal usually mounts to the engine somewhere and often, but not always to the alternator bracket. This makes sure you get the direct connection to the battery which the starter needs since it draws more current than anything else on your car.
The battery Positive (+) terminal connects to the starter solenoid. Again, this is due to the demands of the starter. It requires maximum power transfer from the battery.
 Cable inspection
Look your battery cables over very well for signs of problems. Sometimes you will see a green color on the wire somewhere. This is corrosion of the copper and is called verdigris. It is similar to rust on steel. This is a sign you may need to replace the cable if it can't easily be removed. Even if you can clean it, the corrosion may have traveled up under the insulation and would likely eventually cause problems if it's not already degrading your cable's ability to carry current.
Battery cables are cheap. Yes, they can be a pain to change in some instances, but changing them when you can in a controlled environment might save you from being broken down on the road in bad weather.
 Bigger is better
When it comes to battery cables, while the factory cables are "adequate", oftentimes they are replaced with cables that may not be as large in diameter as the originals. In this case, bigger is better. A larger diameter cable can carry more current safely and with less resistance to current flow.
While welding cable has been used, the insulation is not ideal for an engine environment. There are, however, other sources of oversized cable that have the proper insulation. Still, a high quality, more than adequate battery cable can be found at most auto parts stores.
You should know the length you need before going in. Remove the current cables and take them with you to be sure you have the proper length. You can add a little to the length, but keep in mind, the longer the cable, the more resistance to current flow.
 You're grounded
Be sure there's a ground strap going from the engine to the body and to the frame. Make sure that two grounding straps exist and are also clean at both ends. Most electrical gremlins are due to bad grounds. All too often these bad grounds can be traced to these grounding straps or the battery cables not making a good connection. If all of these connections are good clean connections, you have a solid foundation to build from and will eliminate most electrical gremlins.
 Wiring harness
All too often our cars have had their wiring harness hacked up, cut into, re-routed, and who knows what previous owners of the vehicle did to butcher the factory harness.
The wiring in our cars is often in bad shape from age as much as anything else. Wiring insulation was barely adequate decades ago. Add to that the fact that we add on things that demand more than was ever imagined by electrical engineers back in the day.
Considering that electrical fires happen all too often and our classics deserve to be protected, a new wiring harness should be considered in most cases. Aftermarket companies are making some very nice kits and some are car or class specific.