I’m almost afraid to enter the thread but, well, I’m a poet and I still don’t get some poetry. Some of it just isn’t particularly “gettable” the way prose is.
As someone mentioned upthread, read a poem aloud. Now, some poems aren’t really going to be improved by doing that because some poets, frankly, don’t care about sonics and don’t work to make their poems sonically pleasing. But that tends to be the exception rather than the norm.
What to read to begin to “get” poetry? Well, there isn’t anything wrong with reading someone like Dr. Suess or Ogden Nash. Rhyme and wordplay is extremely common in poetry, and Dr. Suess especially is a master at it. If you really want to work at it, start paying attention to the words he makes up, what words he rhymes and what he doesn’t, what sounds strike your ear as being “funny” and what sounds don’t, how he can sometimes suprise you with an unexpected word and sometimes surprise you by using a word you should have expected but didn’t.
Read his works aloud. Listen to the rhythms. He’ll have reoccuring patterns. See if you can predict the next line’s pattern based on the one you just read. See how often he surprises you, and how much the humor might be influenced by that surprise. (Ogden Nash is the master at this.)
Most of all, be patient. Yes, poetry is rarely the most direct method of communication. Just like a painting is less direct than a photograph. Why would someone spend so long painting a portrait when they could simply snap a Polaroid? Because the painting captures something that the photograph can’t (or, at least, might not). Poetry is the same way. It allows a certain freedom, a certain latitude, a certain use of sonic tricks like rhyme and meter that aren’t quite as accessible within prose’s rulebook. Much of poetry is about imagining an atmosphere or getting a feeling about things that maybe aren’t that easy to describe in direct terms. The point isn’t, usually, what the poem ends up saying–what it all means–but how it says it, and how you respond to it.
And you know what a perfectly valid response is? Snoring. Eyerolling. There’s no reason everyone has to put up with obliqueness and elusive meanings if they don’t want to. If it just seems pointless, well, that means it really is pointless for you. Don’t sweat it.
Just buy my book. 