Here is my technique for dismantling pallets while causing minimal damage to the wood boards, the process is nearly identical for plywood.
First, you'll need several pry bars, the kind with a very flat edge. The sheep's foot ones only really work well once the nail head is exposed - getting the boards separated first is the hard part. If you wanna be extra, you can take one of those flat edge ones and ground it even thinner, like half a mm (you don't want it razor sharp cause it will cut you and the wood too easily). I find the stock pry bars a tad too thick and this mod makes getting into the gap between the decking and the joist much easier.

This kind is great because the handle is stout for hammering. Wedge the blade in between, get it as parallel with the joist as possible, hammer gently until it seats on the nearest nail, and pry. If you cannot get enough purchase on the plywood without crushing it, this is where the sharpened edge comes in. Hit it with the hammer hard and you should be able to cut right through the nail (watch your fingers, wear thick gloves, it'll jump forward when it gives way). You can now get the pry bar deeper for more surface area on the plywood to pull with more force without crushing the wood.
Once you get a corner started, keep wedging around, inserting those flat style pry bars, splitting wedges, or even angle cut blocks of wood.

It kind of creates a virtuous cycle, once you get some of it lifted, you can get more leverage, which lets you pull more nails, get more surface, etc, until the whole piece just pops off. Watch the protruding nails!
I recommend getting one of the pneumatic un-nailers/punch tools if you want to pop the old ones out. You'll want to drape a heavy cloth over a bucket or wide tub to catch the ejected nails, they go flying. Also there's a trick if the sharp pry bar trick fails to get purchase: use the punch tool to drive the nail head THROUGH the plywood out the other side into the joist. Exactly as if you were using a nail gun. It'll create a 1/4" hole in the plywood, but the nail will no longer be able to hold the plywood to the joist. You can do the same with a manual punch but the pneumatic punch is very fun.
