Is there a simple strategy for re-learning Magic the Gathering?
I can think of a few ways to relearn Magic:The Gathering without simply reading the rules. Which, by the way, because of the new stack concept*, streamlining of phases/steps and elimination of many odd special-case rules, is easier than ever in my opinion.


Download the Magic the Gathering Online Demo if you have a PC or if you have an XBox, the Duels of the Plainswalkers 2012 Demo. Since they take care of the game rules for you, you can walk through games, learn the turn sequence and how the stack works. That MtGO link has a YouTube video that walks through the game.
Find a store near you and drop in for Friday Night Magic. It's been my experience that most MtG players are quite happy and willing to teach new players the ropes.


*honestly, the stack isn't that new. ;-)