What is a good strategy for using the Doomsday card?
For half your life, you get to stack your deck and set yourself up for a number of combos.  There's a combo going around that involves Shelldock Isle/ Doomsday/ Emrakul, the Aeons Torn to pop out the Emrakul for free. 

In addition, cards such as Serra Avatar, Beacon of Destruction, and other cards that shuffle back into your library afterwards can be used to stall running out of cards.  Platinum Angel can help keep you from losing the game.

That said, it's a pretty hard card to build around.