I'm going to attempt to show you all how to unravel a sweater:
First, as you are shopping, there are some important things to consider:
Gauge: Most recyclers like to work with only medium or heavy yarn, it's very easy to unravel, I suggest starting with a heavy gauge until you master the process. I prefer DK weight and then I can double, triple or even quadruple the gauge for a heavier finished yarn.
Fiber content: Why waste your time with acrylics when you can find a nice 100% cotton or cotton blend such as cotton/linen/ramie? The price is generally going to be the same, so why not go for the nicer fibers? You can find nice wool if that's more up your ally. I've found plenty of merino wool sweaters.
Seams. The seams are VERY important. You'll need to check the seams to make sure they are KNIT together (or sewn with yarn that is), not sewn/serged with a machine. The machine serged sweaters will give you little strips of yarn instead of a continuous thread. Here is a pic of the inside of a proper seam:

You may find a serged seam at the shoulders, even though the other seams have been sewn/knit with yarn. Never fear! Just cut the seams apart with your scissors, you'll loose a bit of yardage, but not enough to really matter.
Ok, lets get started!

First I cut the tag off gently, stitch by stitch with very sharp scissors (I started out by using a seam ripper, I suggest newbies do the same). Once you've got the tag off, you're ready to get at the good stuff. Oh, don't forget to check if there's a tag inside the sweater on the side seam. The sweater I'm doing now, doesn't.

I ALWAYS start at the bottom of the sleeves. You can see the seam I'm aiming for in the pic above. It is very important to cut at the seam or you won't get a a continuous thread of yarn, you'll get little yarn bits (which make good stuffing by the way). I've marked the seam a bit with little pink dots in the next pic:

So take your seam ripper and just go at it slowly, rip the seam, stitch by stitch. If you're careful, you can find what I like to call "the sweet spot". You can pick and rip the seam until you find the magic thread that, if gently pulled, will separate the sleeve seam, and in most cases, come back down and separate the front/back seam:

Here it is! It took me one snip and I found the sweaters sweet spot. Rock on, let's watch it come apart a bit:

So now, you need to repeat this process for the other arm, front/back seam and neck. My separated sweater came apart in four pieces:

Now let the unraveling begin!
I always start with the arms, going from the top down. Here I've got my sleeve ready in my lap:

I'm way to impatient to properly start it, so I just cut off the edge like this:

Then you'll need to pick at it a bit to get it all on the same row and it'll just start unraveling:

I can tell from the weight of the thread that I'll want to at least double this yarn, so I'm rolling it directly into a center pull ball from both sleeves at the same:

And there you have it! Keep rolling untill you've rolled it all, and start knitting it up!
Now onto
how to measure/skein your yarn!