What you need:

• Crimping tool (for crimping insulated connectors)
• Wire cutters
• Wire strippers
• Butt splice

What to do:

• Strip one wire about 1/2 inch. Twist the stripped part so that it's in a tight, straight bundle and stick it in one end of the butt splice until it won't go any further. Note how much of the stripped portion is still visible, and then take the wire out of the splice and cut off that much wire. The goal is to have no bare wire visible when the wire is in the splice.
• Strip the other wire the same amount as the first one.
• Now you've got something like this:
  
  
• So stick the wires in to the butt splice until they are both in completely:
  
  
• Now, crimp them. You'll notice that if your crimper has options for different crimp sizes, each size has a little colored dot next to it -- use the size with the dot that's the same color as your splice. Crimp each side of the connector twice, on different centers, to ensure a good connection. Make sure that you crimp the metal part of the splice, and not just the plastic boot on the end:
  
  
• Done! Tug both wires lightly to make sure that they do not move in our out at all.