I have great success using a soldering iron, flux and solder. I've only tinned the ends on new cables.

1. Apply flux to freshly cut cable end.
2. Touch with hot soldering iron for 30 seconds (I'm guessing at the time).
3. Touch the solder to the wire end above the soldering iron and once the solder melts and wicks into the cable, you're one.

Note: steel cables take any type of solder. stainless steel cables require a silver solder (I forgor the % silver). The solders I use have "flux core", which adds flux to the joint as the solder is used.

Note: once the solder melts, onto/into the cable, you're done. Don't add anymore for "good measure" since additional solder will drip out. I prefer to finish mine so that solder doesn't appear on the external of the cable, but I know it's wicked into the crevices of the wire bunch.