Step 1: Destruction
Here we see what a few hours of work with a shovel, pry bar, and a ladder will do for you. I ripped all of that mossy mess off and laid it in piles on either side of the shed to wait for a friend with a trailer to take it to the dump. Afterwards I used a magnetic sweeper I got at Harbor Freight to pick up any stray nails.
My goal was to save as much of the wood to use in the construction of the new shed. it turned out that only two or three of the wall studs were rotted so I had quite a few recycled ones to play with. The bottom 2x4 plates that bolted into the concrete on the other hand were complete losses.
Once I removed the wood siding I was able to tie a rope to the roof and, with four of five stout yanks, pull the whole structure down. Once on the ground I removed all of the roof boards and set to work dismantling the 2x4s for reuse.
For those of you that don't believe in the Devil let me assure you that there is one and it lives on this planet in the form of galvanized metal deck nails. These evil bastards are twisted nails that are basically impossible to remove from wood. They're sturdy, they hold wood together wonderfully, but they are your worst enemy if you want to reuse wood. After trying to remove two or three of them with a hammer and then a pry bar I gave up and started cutting the wood apart at the joints with a reciprocating saw with a metal cutting blade. This worked well, but it took me a looooong damn time to cut all of the nails flush with the boards.
If you plan on reusing wood like this you should also plan on buy two or three back up circular saw blades for your circular saw, miter saw, and table saw. Considering the cost of a blade to the price of all new wood, it's worth it.