Sweet dreams are only part of the story
Like any extreme activity, it requires the nerves of steel, good choice of timing, location and the absence of suspicious cops. All this however is easier to achieve, because you are, well... asleep, so you can trust the unseen powers to take care of the rest. Long & restful sleep is by no means guaranteed, but perhaps somebody will take your picture and you'll wake up famous.
Location, Location, Location
The best site to explore (or to learn this useful skill) is Sleeping Chinese. It's a constantly growing collection of impossible sleeping positions:
(images credit: Sleeping Chinese)
Ignore the crowds
According to this site, Japan's Public Sleeping is a constantly evolving art:
(image credit: Jeff Tsai)
Schools are made for sleeping
Studying obviously leads to extreme mental and physical fatigue:
Learn from kids
Of course, children are "professional" sleepers:
Cats have no competition, though.