Using wire strippers, strip the ends of the red and black wires connected to the the new battery back about a 1/8".

Twist the strands of the spliced wire together.

When the connection is hot enough melt solder on the opposite side of the wire to the iron as shown in the image. Do not melt to much solder.

Repeat this process with the other wire.

This video provides basic instructions for splicing wires using crimping and heat shrink technique.