Very carefully. 
 
But in all seriousness, if you can start with Link to the Past, DO IT.

really you can veiw each game as a separate non related story. at least for me its too much of a hastle to piece them all togother. the angry video game nerd made a video explaining how each one is tied together. here it is 
http://www.youtube.com/watch?v=cHIP9UtkQDQ

Fellow dudors, I really wanna do this and I thought about it for a long time without coming to a decision - so I am passing this over to you guys. I indent to play through all games on my GameCube since it's possible to play through all Zelda games on that console except the DS games. I already purchased Zelda I, Zelda II, Ocarina of Time, Majora's Mask, The Minish Cap, A Link To The Past (including Four Swords), Wind Waker, Link's Awakening DX and Phantom Hourglass. 
I'll probably buy the missing ones (Four Swords Adventures, Twilight Princess, Oracle of Seasons, Oracle of Ages and Spirit Tracks) over the next one or two months. 
It will most certainly take me some months, maybe even 1-2 years to play through all of them but I intend to keep everyone on GB updated.  
So thanks for helping me out with this one!

" Very carefully.  But in all seriousness, if you can start with Link to the Past, DO IT. "