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Make a dishcloth out of dishcloths (in this case, Chux SuperWipes) by cutting into 1-inch strips and tying together and knitting into a dishcloth. (Or crocheting would do as well)

What I find of note in this is the how-to-cut T-shirt yarn instructions which are part of this article. This method uses the whole t-shirt, not just the torso. This is much less wasteful than other methods I've come across.

This covers both rag-yarn making and crocheting a basket. This yarn-making method has the added step of twisting the yarn (or double-twisting it) before it's rolled into a ball for use. This would make the yarn shorter but sturdier. The double-twist method probably needs two people, but would give the most robust yarn.

This method of making rag-yarn can be done with shorter strips; the strips are joined with slip-knots.