I do this from time to time, whenever I'm out junking and find a suitable sweater ... rarely with a specific project in mind. If the sweater is in decent shape, made of quality yarn (wool, cashmere, silk, etc.), and isn't abused or felted, I buy it.
The subject of this example is a 100% wool sweater from Goodwill, brand new with the original store tag, in a fantastic greenish-brownish-gray. It's enormous ... which means that it will yield a LOT of yarn.
First thing is to disassemble the sweater by unraveling the seams. I only buy sweaters with chain-stitched seams, which are fairly simple to identify and take apart.
With the sweater taken apart, all that's left now is find the yarn end on each piece, work it free, unravel the pieces, and roll up the yarn,
Alice was helping.
When I'm unraveling, I roll each piece of the sweater into its own ball. For this sweater, there is a yarn ball for each sleeve, the collar, and the front piece. The back piece was rolled into two balls because it had a hole in it, which broke the yarn at that spot.
How much yarn did I get from this enormous sweater, you ask? Exactly 856 grams ... which equals seventeen 50-gram skeins, if I bought this at a yarn shop.
Before I use this yarn to make something, I will roll it into skeins and wash it ... to relax the kinks and make it easier to work with. For now, though, it's stored away in balls, just like you see it, with the rest of my yarn stash in the sewing room, along with the label from the sweater so I remember the fiber content.
If you're inclined to do this yourself, and you need more detailed instructions, you can find a really great tutorial HERE.