Georgie,
If you are really industrious, you could strip some of the insulation back and solder on a new length of speaker cable (I'd also have some heat shrink tubing on the new end ready to slide over the soldered connection and shrink on). That will give you probably the most secure and best connection.
However, simply connecting the leads of one wire with the same leads of another using wire nuts should give you a very good connection and one that is completely fine for good signal transfer. Not to mention that it is much easier to do than soldering.
Mark
Aperion Audio Guru