Each stadium will be taken apart by hand, piece by piece.
From Sandomir:
The wreckers will arrive at Shea Stadium soon after the Mets’ final home game in late September or sometime in October. In February or March, Yankee Stadium’s dismantling will begin. The old ballparks will be taken apart piece by piece over two to three months with hydraulic jackhammers, blowtorches and grapplers.The article also points out that pieces of the stadium, such as the seats, bricks, and signs, will be sold, most likely for a very high price.The concrete will be chopped up, pushed toward the middle of the fields and removed by trucks. The steel girders will be cut out, cut up and carted away for salvage.
Shea will then be reclaimed as part of the parking lot, and Yankee Stadium as three baseball fields surrounded by 12,000 trees.
Also at the New York Times, Ben Shpigel has a great article about Shea.
From Shpigel:
By any objective standard, Shea is bleak and outdated. It has not aged, shall we say, gracefully, its imperfections and architectural shortcomings growing more prominent over the years, particularly as glorious baseball-only parks have sprouted around the country. Those flaws are now magnified by Citi Field, the Mets' new home in 2009, whose beatific presence beyond Shea’s right-center-field fence prompted Ron Darling, the SportsNet New York analyst and former Met, to make this comparison: “It’s like driving a VW bus with a Maserati in the lot.”That article brought a little tear to my eye. Wonderful, wonderful stuff.
---
“It’s dilapidated and obsolete, sure, but I could say the same thing about the apartment where I grew up, in Bayside, Queens,” said Howie Rose, the Mets’ play-by-play broadcaster on WFAN. “That apartment was home. My memories there are happy, warm and indelible, just like they are from Shea. To me, Shea is home.”