General- Expose and clean the ends to be joined for 1/2 to 1 inch with fine sandpaper. You need a small soldering iron and electrical or silver solder wire. Twine the two ends together. Do not break the fine, individual wires. With one hand Apply the solder wire end to the area to be joined, and the hot iron tip to that same point with the other hand. When the solder liquifies, dress the twined wires with the solder as neatly as possible. moving the iron up and down and on all sides of the joined wires. W.when the join cools, wrap with electrical tape.
May take a little practice. Try it with scrap multistrand wire of about the same gauge first.
A more technical treatment is here: Soldering

If this link doesn't work, put "soldering wire" in Google. It was the first item. Acrobat needed.
www.mil.ufl.edu/4744/labs/lab2_f02.pdf