I've done this many times now, it's not that hard.

Start by holding the spring and winding it up in your hand. Then carefully grab it with a pair of needle nose pliars making sure it does not unravel. Place it inside the pullstart, and put pressure on it with your remaining fingers so it doesn't fling out and try to kill you. Make sure the outer tab on the spring is locked into it's little groove thing in the pullstart housing.

Now wind the cord around the bobbin making sure you wind the right way around. You may want to replace the cord as you will have to shorten it a bit to take up the slack you will have when you finish.

Now place the bobbin in the pullstart and rotate it till it catches on the inner tab of the spring. Clip the piece of plastic on the pullstart that prevents the bobbin coming out.

Now pull the knot out of the T handle with a pair of needle nose pliars, and pull the cord out until there is a little tension, tie a knot and snip off the rest, you may want to add a drop of CA glue to the knot to ensure it doesnt come undone.

And voila! You have sucessfully rebuilt your pullstart!