In the Poets At Work workshop, we’ve been photocopying a spread from the encyclopedia (just open the book at random and work with whatever you get.) This then becomes the lexicon for your poem; you can use any sentence, phrase, or word on the page, but you can’t add anything. My own technique is to read through it and copy down all the phrases that seem interesting to me, leaving space between each one. Then I cut them apart and begin to piece them together. The idea is not to make conventional sense, but to look for ways to get new meanings. The encyclopedia is good because of the variety of topics (I recently got a spread that included the Serengetti and the Sermon on the Mount!) Some poets stay true to the lines as written, even as they re-order them, while others go wild with splicing and re-organizing. I’ll post a sample of my own attempt below so you can see how it might work.
Cut-Up Poem #2: Sermon on the Mount
Search for extraterrestrial life:
an empty or null set.
Trickster, sky god,
lord of the desert, master of storms.
As a wild animal artist,
looking for non-random patterns,
lions, leopards, elephants, rhinoceroses
could be matched with stones in a sack.
The Twilight Zone,
a blueprint for Christian life.
Movement has been away from linguistic unity.
Who desired to transcend it?
About the Black Death:
Intelligent beings increasingly mechanized;
many of New York’s streets
in constant shadow.
Twelve tone music,
notable for its theory of prophecy.
Two hundred species of birds: a new law of love;
notion extends into the infinite.
© Terry Wolverton, 2007
Writers At Work 
This is reminiscent of an even more random technique from the dada movement in France during World War I. Tristan Tzara explains it in a poem called “Pour faire un poeme dadaiste” (How to Make a Dada Poem). Here’s my (rapid) translation:
Take a newspaper
Takes some scissors
Choose an article from the paper that’s about the same length you wish to give your poem.
Cut out the article.
Then cut out carefully each of the words that make up this article and put them in a sack.
Shake gently.
Next take out each cutout one after the other in the order they happen to leave the sack.
Copy down conscientiously.
The poem will resemble you.
And there you’ll be, “an infinitely original writer with a charming, though misunderstood by the common herd, sensibility.”