Materials:
2-3 old dress shirts
scissors or a rotary cutter and mat
No 9 crochet hook
A lot of rage (optional)

So, here is my how to:
You need to transform old work shirts (or current work shirts if you are REALLY mad) into a ball of rags. To do this, cut off all the buttons, the arms, the cuffs and the collars.

I cut off the arms, cutting out the seam at the same time:

You can leave the seams in, but it will make for harder crocheting later.

Once both sleeves are off, lay the shirt out on a large flat surface and start cutting a thin strip around the outside of the fabric.  As a measure, I used my thumb for relative consistency.  Don't worry about being exact.  Varying widths add texture (or so I tell myself).

When you get near the far edge, you are going to cut in a gentle bend, so that the shirt is one piece of fabric (think spiral).  You may need to trim a bit of excess off the corners.

You want to cut in as much of a spiral as the shirt will allow.  The armholes are bit tricky, but just cut around them as much as possible.  If the line breaks, tie the two ends together.  Its not an exact science.

Once the body of the shirt is done, start on the sleeves.  Cut along the flap in the cuff to create one flat piece of fabric, like the body of the shirt.

Then, follow the same principle of cutting in a big spiral, trimming corners as required.  Tie all of the pieces together and wind into a ball. When I finish with one extra large men's shirt, I am left with a large ball of "yarn" and a small pile of wastage:

Obviously, a smaller man means a smaller ball.

I then use the ball of rags to crochet the bucket.  One shirt is enough material to crochet an 11" diameter circle for the base using a double crochet with a 9mm crochet hook.
 

I didn't use a pattern for crocheting the bucket.  You will need to increase and decrease appropriately to get the shape right.  About.com is often cited for good instructions, and I often use You Tube or my Happy Hooker book.

I used a American double stitch (UK treble), it made the bucket quite stretchy and loose, which is great for storing it away when not it use.  For a more solid, bucket use single crochet (UK double). 

It is worth the hard work, as I crochet out my frustration, have a nice new bucket, and my dearest husband doesn’t lose any appendages!  Win/win, I think that's called.