First thing you do is go to your local thrift store (or possibly your own closet) and find a nice soft knit wool or cotton sweater (whatever type of material you want or like), just start reading the labels, you will find some. I would start with a sweater that is a solid color, this is the easiest to "recycle". Now that you have found the perfect "yarn" and BEFORE YOU LEAVE THE STORE, check the seams. If the seams are surged together put it back, surging cuts the yarn at both ends of the row so when you pull it you will just end up with a bunch of yarn pieces. You will want one that is seamed together with one long thread and when you get it started you can pull it out in one long thread, like opening a bag of dog food.
Here is a picture of the type of seam you want (I already started pulling this seam out, see how it is coming out in one strand)...
Now you will want to get a small pair of scissors or a seam ripper, this is what I use..
Next you need to figure out which end to start pulling the seam thread to unravel the seam. Usually the best place to start is on the sleeve cuff and that will unravel all the way up the sleeve and down the side in one long pull..
Pull the other side seam and you should be able to open up the sweater...
Next is usually the collar, just find the string that is holding the seam together and start snipping and pulling, finding the start or end of the collar seam can be impossible, so just start where ever you can (remember not all sweaters are put together the same way, so take a good look at the construction of the sweater. Sometimes you will start to pull a seam and get to a point where you will realize you need to pull another seam before you can finish that seam...)
Oh yea, don't forget to carefully take off the tag...
this is something you may want to keep so you know how to care for your "new" yarn
Now for the shoulder seams and soon you should have all the pieces of the sweater apart, front, back, 2 arms, and possible a collar... (here is the sleeve )
Now it is time to start pulling and winding you "new" yarn. If you have ever made a mistake while knitting then you already have experience at this. You will want to start at the top, find the end, and start pulling. Sometimes you have to carefully snip off the bind-off row to get things going.
Once you find the end start pulling and winding (a ball winder would be a nice thing to have.... unfortunately I don't have one so I pull a little, then wind a little, then pull a little, then wind a little..... Or I will have the kids hold and I will pull and wind at the same time.)
And when you are done you will have 4 or 5 big balls of yarn (ok, obviously not from the same sweater, but I think you get the point.... and this picture is not all the yarn that came from one sweater, it is missing 2 big balls of yarn that I used to make a little stuffed froggy for the kids, that they lost!)
If you are worried about how kinky the yard comes out, don't worry. The yarn will either relax on it's own or you can soak it for a while in the bath tub and hang to dry, or just do what I do and say heck with it and knit with it, usually can't tell it is kinky, especially after I have blocked or washed my new item once.
So in the end I pay about $4 for about 4-5 balls of nice soft yarn instead of $4+ for one skein of cheap acrylic yarn.