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.

Using a soldering iron, apply heat to one bare wire connections you have just made.

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.

Once connection is made wait for it to cool off and gently pull each side of the wire to test durability.

Repeat this process with the other wire.

If you do not have access to a soldering iron, leave the old battery wires attached to the motherboard and simply splice the new battery's wires to them.

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