In Anastacia?s music video for "I?m Outta Love", there are several
shots of her moving her hips. When she does, her body looks like it?s
made out of rubber; she moves like a slinky. It?s a very pleasing
image.

How does she get her hips to move like that, and how can I learn to do the same?

Hey there! I've been a salsa dancer for years and we do a lot of work
on hip-rhythm. Try this: stand with your feet about shoulder width
apart, then bend your knees slightly. Keeping your feet and upper body
still, push your hips forward as far as is comfortable, then return to
center. Now repeat the action but to the left, then the back and then
right. When you have a bit of confidence, try to move from one
smoothly into the next - forward, left, back, right. The final step is
to perform the motion in a smooth rotation of the hips. This will all
take practise, most people can't move their hips much at first.
Advanced techniques (which look seriously good) include rotating your
hips in a figure of eight motion (keep your knees bent for full
impact!)