To write an abstract poem, it is important to understand that it is not the meaning of the words that are important but the feeling, the sound and the impact of the words on the reader or listener. You do not have to rhyme any of the words and, most importantly, it does not have to make sense. You are creating something intangible yet beautiful. One technique is that of William Burrough's (famously also used by David Bowie).
Finding and Using Words
Take your old newspaper and begin cutting out words or sentences that you like. It doesn't matter what they are about. Try to use several different articles in the paper for this, so that you get a good range of words for your poem.
Arrange the words in any order you please, trying to make short sentences out of the words that you have. You can also add your own abstract words at this point.
Once you have created something that you like, make sure that you haven't tried to make it make sense. Remember to think about the feeling, sounds and impact that you wish to convey to the reader or listener. Here is an example:
Bountiful birds ran tragically on bypasses
Conical suns let the elephants by
Writers dipped into a hillside
Merriment abounded on the psychotic stars
Try out another technique such as making a "sound poem," by just making sounds out loud, repeating them, changing them and then putting them altogether in a "performance." A twist on this technique is using words from a made up language, nonsense words or even saying words backwards.
Remember, the feeling is more important than the meaning.
Say the poem out loud---you will know if it sounds good.
Try it out on friends and family.
Publish the poem online to get feedback.
Use any form of written word to cut up---it could be a takeaway pizza menu, an old book, a travel guide, a leaflet, etc.