I'm not 100% satisfied with the results yet, but this is only the first try.
I shampooed her gelled hair with mild dishwashing soap and conditioned with Dove oil-free conditioner. I let it sit for about 5 minutes and rinsed with very hot tap water, which softened the curls a little.
Next, I combed through with a fine comb, straight on top and curly at the ends. I let it dry with a soft ponytail holder over her head, so the top of her head would stay smooth.
When dry, I used an alcohol-free gel to help the wisps, and finger styled the curls.
Next time, I think I'll boil perm slightly, to straighten the roots a little more. Also, I need to fix her eyelashes next.
You can see a few more photos of Adele on Flickr.