First, remove the black plastick handle. It should come off into two parts. One will remain attached via an accelerator cord.

Next, push your replacement cord through the hole it normally comes through and then carefully get it to loop around the white round pull start mechanism. Only loop it once.

Then pull the starter rope while applying tension to the end. It will wind up the white pull start mechanism.

Then tie a small not at the end of the rope and push it into middle of the white pull start mechanism. You will see a small place for it to push into.

Then slowly let the wound up pull mechanism pull the rope in. If done correctly it will wind up the rope for you.

Then reassemble and should be good.