I do them by taking a text file and cutting it into quadrants. Then I reverse two of the quadrants (upper right for lower left, for example) and see what I've come up with. Another method is called a fold-in, and it is different in that it combines text from two different files, rather than just rearranging the text in a single file. This produces not only new sequences of words, but also new words (since some words are sliced in two), so the first thing I do is usually to run a spell check.
Originally, of course, all of this was done with typewriters and scissors and retyping. I prefer to do it on a computer screen, using a text editor (such as QEdit for DOS, or emacs for Linux) which allows the selection of rectangular areas of text. Word allows this also, though the feature is not widely known. Just select text with the mouse while holding down the Alt key.
Once I've rearranged (or combined) the text, I start to fiddle and rewrite and massage, until I get it where I want it. The amount of fiddling varies, but the general rule is to do as little as possible.
I like cut-ups, for a few different reasons. They recharge my batteries. U-town came out of doing cut-ups. One day I was doing cut-ups, then I was writing about the Wasserman family, then I was writing about Vicki running away from home and ending up in a weird donut shop that later became Duffy's.
Later, when I was trying to figure out how to get out of a cul-de-sac in the story, I did some cut-ups, and eventually the answer came to me.
I also like cut-ups since they are the only really short form of writing that I'm good at. I can't write poetry, and even my "short stories" (like "Always Crashing in the Same Car") aren't all that short.
I also like them because sometimes they're really funny, at least to me.
Some cut-ups are better than others, and at one point I went through the second batch (the ones I did while I was waiting for U-town to disentangle itself) and picked out the top ten, and here they are.
Top Ten Cut-ups: