Let me tell you what NOT to do, so you can avoid it.
DO NOT melt the solder with the soldering iron and drip it onto the wire. This is called a cold solder joint. It will hold the wires together, but it won't conduct electricity.
I disagree with Guest Q's advice to "Apply the solder wire end to the area to be joined, and the hot iron tip to that same point." My advice is to hold the solder to the top of the joint, and bring the soldering iron to the bottom of the joint. You want the hot wire to melt the solder, not the soldering iron.
Since you're just soldering cables, you don't need to worry about excessive heat ruining delicate electronic components. If you get ambitious and want to solder electronic components, come back and ask about heat sinks first.