Step 3: Pop and hang
Once everything's all dry (yay!) and you're confident in the doily's stability, it's time to pop the balloon. Grab something sharp, and poke a hole. The glue will hold the balloon agains the doilies, but the tension and pressure from the stretched balloon will eventually cause it to pull away. It's fine to get in there and do some pulling, too.
And you're all done! Enjoy your handiwork, and then hang that sucker. Grandmotherly accessories never looked so good.