Sometimes you need to lengthen wires, and sometimes you need to split one wire into two or more. This is called splicing, and it's is a great skill to add to your arsenal.
Cut a small piece of 1/8" heat shrink. Make it just long enough to cover your joint - maybe 1/4"-1/2" long. Slide it onto one of your wires, and move it down out of your way a bit.
Strip about 1/4" of shielding from the end of each wire. Give the wires a twist so the strands are all neat and tidy.
Bend the tips of the wire so they make little hooks. Hook the two hooks together.
Twist the ends of the hooks around and around the wires to make a little wire ball in the middle. I like to twist one side clockwise and the other side counterclockwise.
Make this connection so mighty and tough that it doesn't come apart when you tug on the two wires. Twist it up tighter than a car salesman's handshake. Make it so twisty and tangled that the wires barely even need to be soldered. They might not even notice if you forget to solder them altogether. They have become One Wire.
Heat up your soldering iron to 750 degrees (or for 3-5 minutes, if you don't have a temperature gauge). Make sure the tip is nice and clean.
Press your soldering iron right onto the wire connection and wait a few seconds for it to get nice and hot. Unspool a bit of solder and touch it right to the knotty wire connection. The solder will melt and flow in and around your connection until it fills in all the spaces and creates a little shiny ball of solid metal. Lift your the solder away, then remove the iron.
Finish by sliding your heat shrink over the solder joint and shrink it down with a heat gun or the side of your soldering iron.
Used when you need more wires than you have pads or solder holes available, or if you're connecting multiple strips to the same pin.
Strip slightly more than 1/4" of shielding from the end of all three wires. Twist two of the wires together with the tips pointing in the same direction.
Slide a piece of heat shrink over the double wire.
Hook the third wire onto this twisted pair so they're strongly connected, and twist the wires around each other, just like you would with a 2-wire connection. You'll end up with a Y-shaped junction.
Heat your soldering iron to temperature (750 degrees, or for 3-5 minutes) and make sure the tip is nice and clean. Press your soldering iron tip to your connection and wait a few seconds until it gets hot. Then, feed in your solder so it melts flows and and fills in all the space in your little wire ball.