The heavy tapered tool you see in the photo is an original soldering iron. You would heat it up in an oven or with a torch and use it to melt solder. This technique is sometimes still used by sheet metal workers today.
Most soldering irons today are electrical, and you can even get them with carefully controlled transformers that will give you exactly the temperature you want.
For emergency repairs you can even purchase soldering tape that you wrap around a wire joint and then melt it with a match.