First attach the strap to the tag. Do this by putting the strap through the slot, then taking one end of the strap and passing it through/between the other side of the strap. Pull and it will snug up to the tag.
Now, repeat on your tag handle, this time instead of having two ends of a strap though, one end is a strap and one end has the tag, you pass the tag through the other end of the strap. You will have to apply some force to stretch the strap enough to get the tag through. It won't ever wiggle itself free.
I tried to find some pictures online but couldn't. It's the same as attaching a camera strap though, just you end up doing it twice.