As a kid I remember memorizing a few poems, mostly for the heck of it -- The Walrus and the Carpenter was one, and then there was some rendition of Cinderella by Roald Dahl (which was heaps of fun, as I recall). There are a couple of poems that I've recently discovered I've mostly memorized, just because I read them often enough. I've liked it, knowing that a few of my favourite poems have taken up residence in some little part of me which I can always come back to.
There's only been one poem I've intentionally memorized in the more recent past, and I think it helped that it had a very definite meter and rhyme. I think it might be slightly harder with free-verse because then you have to make a judgement call on how you want a certain line to be said. As for technique I just tackled it verse by verse, going over it a bunch of times. Repetition is key here, I think. And stubbornness perhaps. I've never recited a poem to an audience though, but I have recorded a few readings. Actually, I've found that listening back to the takes is really helpful to hear which words aren't being enunciated well enough, and to pinpoint where the flow is awkward or where the cadence doesn't work. So that might be a good way to practice.
I think force memorizing isn't the right way to go.I memorize a lot of things spontaneously ,by liking them much and reading over and over again .Same goes for recitals ,when I consider something I am reciting great I have no stage fright and even enjoy accenting and sharing what I learned with others .
I did this when I had a cleaning job and was so bored I needed something to occupy my mind. Being able to recite a few Shakespearean sonnets has been fairly useful, actually. If only to appear a bit educated at parties....
It's always easier to remember something you have written down, so when I need to memorize a poem that's my first step. If you just take the poem a few lines or a stanza at a time (depending on the poem's length)then you can tackle the whole thing systematically. Also if you hear someone else recite it it should stay in your mind better. I just started trying to memorize the prologue to the Canterbury Tales in Middle English, so I really want to find good audio of it. (I don't really know how to pronounce Middle English properly!)
Some, yes, - I go from poem to poem and sometimes even just lines, but I have a few I'll always remember, like Jabberwocky or The Stolen Child. I like memorising poems and being able to quote them. I'm going to try doing it for my own poems when I get the time, as I believe it'll really help with sorting out word choices, and editing and the like. I haven't ever memorised poems for speaking to an audience - just for selfish reasons, really - but I've heard that it helps with speaking and articulation.
I just usually reread them - it's easier with rhyming, traditional forms. I haven't memorised a full free verse poem yet, so there's that. Like `HaveTales-WillTell said, #Elocutionists are great for spoken poetry.
The ease with which one memorizes a poem depends upon length, difficulty of language, and emotional attachment. Say for instance we compare a piece of free verse with metered work (e.g. something like Mina Loy's "Lunar Baedeker" versus Frost's "Stopping By Woods On a Snowy Evening) obviously, Loy's piece would be exceedingly difficult compared to the masterful simplicity of Frost. A style of writing which utilizes multi-syllabic rhythms through heavy words would very much be hard to memorize, regardless of whether metered or meter-less.
I recommend for those staring off with recitation with a combination of simple pieces: Ha Jin's "Ways of Talking", Shel Silverstein, Dr. Seuss, Robert Frost. Metered poetry is often easier to memorize because of the naturally anticipatory language but there are some difficult pieces out there that use obscure feet and combinations of traditional forms.
It's definitely a good idea to start with something simple, that you like, and is not too long.
I've done it many times. I was on the speech team, and I competed in the poetry rounds every year. I would learn a ten-minute presentation every year, usually consisting of three or four poems and introductions / transitions for them. I have also memorized poetry for my own fun. Back in junior high, I walked to school every day, a journey of roughly fifteen minutes. I spent the time, one year, learning The Lorax. In that case, I would try to add one new stanza every day, and then recite from the beginning to that stanza, until I eventually finished it. I now know the whole thing, and performed it live at a local Barnes and Noble (they had a weekly poetry reading by anyone who signed up). In high school, I also learned The Charge of the Light Brigade for fun. In each case, I created a persona for that piece. This included a distinctive character voice when the poem called for it, and sometimes a unique voice for my narrator, to better convey who I felt he was. That helped me appreciate the cadences of each voice, as well as any humor in the pieces. In speech, you are also supposed to establish "focal points": places on the opposing wall that you look when you are a specific character. This helps to cue the audience as to who you are playing. You might not be in a position to do this, though, if you aren't reading in a room to an audience. I can tell you that we were graded in part on projection, enunciation, and vocal color, so we had to learn to speak clearly without becoming automatons... Does this help at all? I'm happy to answer any more questions if it'll help...