My method is, I look through every issue when it first comes. Then I set it aside in the piles of other magazines and stuff waiting to be read or attended to. When I have some free time to read, I randomly grab whatever issue is handy. I read the easy things -- the movie reviews and "Shouts and Murmurs" -- first, sometimes the contributors' notes and letters to the ed, plus whatever bylines I know I'll like (Sedaris, Lepore, Gladwell, Levy, Lane, etc.). If something else really grabs me, I might read it right away. Otherwise, the issue gets added to a towering slippery stack of magazines that just keeps getting bigger and bigger until I can't stand the clutter anymore. Then I go through the stack, trying to be ruthless but repeatedly getting sucked into actually opening each magazine, however old the issue is, and glancing through the table of contents. I try to force myself to throw it out no matter what, especially if it's from a previous year. But I find myself thinking, geez, I really should read that article about the oil spill, or Hillary Clinton's chances in the presidential election, or whatever, and rip it out. Then I have a stack of articles that I think I will read when I'm stuck waiting in line at the bank or something. Some of them, I do get to. But others get tossed around the car or purse until they're so ragged and dirty I finally decide can't stand to have them around anymore. So, finally, I toss them.
That's the life cycle of a New Yorker article for me.