I have been playing MTG for a few months now and was told that there is a story behind each set of cards. I have several small bits of the story that came with the decks, but I would like to read the full story and see if I can construct my themed decks to match how they would be in the story. Where can I learn more about the back-story to these cards?
Wizards has short storyline summaries shown here:
Unfortunately, this is an old page and hasn't been updated since Mirrodin.
Wikipedia has a fairly comprehensive outline of Magic: The Gathering storylines that are helpful in getting a handle on the general theme of each set.
However, if you want to get a handle on affiliations of specific characters and creatures within their settings, I highly recommend starting at the MTG Salvation wiki Category:Storylines.
I don't read them myself, but every year Wizards of the Coast releases novels which are a companion to the latest Magic sets/block. If you want the complete "story behind the game", this is probably the best path to go down.
Here's a useful link: http://en.wikipedia.org/wiki/List_of_Magic:_The_Gathering_novels
The Magic Daily site also has quite a fun column called "Savor the Flavor" which contains essays on the latest sets from a storytelling and flavour perspective - you can't get a full picture of what's going on from reading it, I don't think, but it may appeal to someone who is interested in the ongoing story aspect of Magic, not just the mechanics of the game:
The Wizards of the Coast website has a page within it that contains the full story, minus the novels. Heres the link.