After completing Mass Effect 3, a 'Legend' save is created prior to assaulting the Cerberus Base. To experience the Extended Cut DLC, load this save game and play through to the end of the game. The Extended Cut endings will differ depending on choices made throughout the Mass Effect series, so multiple playthroughs with a variety of different decisions will be required to experience the variety of possibilities offered by the new content.
This is from the official Mass Effect website. It essentially says that no single save will give you all of the endings and indicates that you may need to play the whole series multiple times to get them all.
It is important to note, however, that BioWare stresses on its official Extended Cut FAQ that:
The Extended Cut is an expansion of the original endings to Mass Effect 3. It does not fundamentally change the endings, but rather it expands on the meaning of the original endings, and reveals greater detail on the impact of player decisions.