We start off each lesson with a shared reading of a poem. I let the kids enjoy it and make comments. I will also quickly point out any tool used in the poem, alliteration, etc. Then the kids can go to centers.
Poetry Table
One is a table with lots of poetry books. They get with a partner and read through the book, marking poems that they like. On the front of the book they will put a sticky note with the title of a poem. They can share these at the end of class, and I use some to make into transparencies for shared reading.
Poetry Window
I put tape around a window and the kids go over and write down things they see outside. This is to collect "seeds" for future writing.
Doors to Poetry
I have the five doors to poetry center. See Georgia Heard's book Awakening the Heart.
Poetry Free Write
They compose poems
Poetry Copying
They copy down a favorite poem, or even favorite phrases in a poem and illustrate. We recently did "Sunflakes" by Frank Asch and the kids chose the words or phrases that made a good mental picture. They copied them down and illustrated it.
I hope some of these ideas are useful to you. Here are some good titles:
Animalia is great for alliteration
Hailstones and Halibut Bones is wonderful. Pair it up with My Many Colored Days by Dr. Seuss and Color Dance by Ann Jonas, then the kids can write their own color poems.
Our school improvement plan last year was to include more poetry into daily work for our kids. So here are a couple of my suggestions:
I hids a ladybug piece of notepaper (laminated) in a student's desk each morning. That is known as the poetry bug. If they catch the poetry bug, they get to not do D.E.A.R. time like normal. Instead, they get to go to a wall in the back of the room that has a variety of poems laminated and on velcro stuck helter skelter for them to choose from. They take one or several to their seats and read those for D.E.A.R. times. they love it because they are allowed to get up and down as often as they like to swap poems. I change the wall for each season. It was a lot of work to copy the poems and put nice colour behind them before laminating, but well worth it.
ALso, I created centres where the kids get into more depth with longer poems. There are six laminated copies of the poem at the centre and six laminated instruction sheets. the instructions start with an activity that goes with KNOWLEDGE level thinking on bloom's taxonomy and they work up to the Synthesis and Evaluation levels. I taught students about the different kinds of thinking at the start of the year and posted a ladder with KNOWLEDGE on the bottom rung and a little stick man that we take off and stick whereevr is appropriate when I ask them a question. (We refer to it once in awhile just to remind them of what level I want in their answers). The centres work really well because the kids can work independently while I do a mini lesson or guided reading with another group. I can e-mail them to you if you'd like!
I love the poetry slam idea. I amy try that this year too!!!
On Mondays we spend the most time on the poem. Reading through it and decorating our page for our folder. Tues-Friday mornings we read through it once or twice during calendar. I often write them in 2 colors alternating each line. Then, I will say boys read the green lines and girls read the yellow- or people wearing jeans read the green lines etc. It just makes practicing more fun. Also, Friday afternoons performing them takes about 20 minutes-- we all clap for each group or person. If they had a hard time we recognize that and wish them better luck next week. Also-- you may want to pre number your poems or have the students number the pages as they go. Later in the year we get out our folders as a "filler" activity, I pick a student and they tell us which poem we should all read. It is easier for everyone to find it if the pages are numbered. We always sit in a circle on the last day of school and do this. They are so proud when they still remember it and don't even look back into their folder! You can make the whole area around your poem a poetry center with magnetic poetry, stamps to write their own poems, frames and highlighters to find specific words or sounds. Sometimes I'll laminate a smaller copy of the poem and cut it in strips or like a puzzle and they have to put it back together, I call this "poetry puzzlers." At calendar in the morning I also read 2 or 3 poems from Shel Silverstein or Jack Prelutsky. They LOVE this because they are such SILLY poems. Hope you have fun with poetry I LOVE IT!!
For our poetry unit we do something super fun and extremely motivating. I always start on a Monday morning and when the students arrive they see the class clothesline lined with balloons. After careful inspection, they realize that there is a small piece of paper rolled up inside of each one. I write a different type of poetry on each slip of paper and place it inside the balloon before I blow it up. Then I use a big marker and write a number on the outside of the balloon so that I can keep track of what type of poetry is inside of each one so that I can plan lessons accordingly. I hang them up on the clothesline. Each day, we POP a balloon. Out flies he piece of paper...which is quite exciting for all. We unveil the slip of paper. I always then teach them about that type of poetry, read samples together, and the they go and try it out on their own in their Writer's Notebooks. They choose which ones to publish and we are currently publishing them in these small hardcover blank books our school purchased each student for our Young Authors Month. It is so fun to discover poetry this way. Have fun!
I like to use poetry for a lot of different things. My students' favorites are for creative drawing. I will read a poem aloud to them several times (ones that have a lot of description). They draw a picture to go along with the poem.
Today I did a creative writing with one. I read a poem aloud. It was about a kitten who was playing with the ornaments on a Christmas tree. They had to write a story telling what happened (good for cause/effect) Also, we have been talking about how a title of a story can help you to figure out the main idea of a story, so they had to come up with their own title that would tell someone what their story was going to be about. We had a lot of cute adventures about that kitten and the Christmas tree.
I have a lot of neat poetry books and try to incorporate them into my classroom each week as well. I love Jack Prelutsky and Shell Silverstein. I have a book (something like month to month poems), a poem a week, holiday poetry books, etc. My kids really do enjoy poetry! Maybe they could compile their favorites into a booklet. I use poems for read alouds, creative writing/drawing, rhyming words, handwriting, etc.
I hope this helps a little. 
I have just done a bulletin board that says BUDDING POETS. I have a carson delosa book that has a design of flowers growing out of a pot. I blew that design up so that it fits on legal size paper. I put lines on the pot so that they students can write their poems on the pot.
If you don't have this book...i bet someone in your school does. It is very popular in my school. IF not, you can always have the kids make their own pot designs and flowers.
Hope this helps.
I teach poetry similar to MIteach... actually, that's probably because I also use a book by Georgia Heard, but it's called For the Good of the Earth and SUn. I'll have to look into the one MIteach mentioned... the one I use is SO valuable. After reading it, I feel like I am teaching so much more than poetry when we do poetry in our room. In this philosophy you're really not teaching "types" of poems, as much as you are teaching a poem as a vehicle for communicating tiny, powerful, intimate, and important thoughts.
I explained what I do in detail and also posted lots of my lessons and books on this thread:
http://www.proteacher.net/discussions/showthread.php?t=27910
As for a way to teach both reading and writing, I've found great success with having a poetry journal where kids both paste in favorite poems by famous poets AND write their own. For example: If, in one mini-lesson I was showing them how poets make their poems mean different things by breaking the lines in different places, I would have some good free-verse examples of that. They could choose one that speaks to them, paste it in, and then try it out for themselves.
Also, through out this school year, I've been doing something that I haven't tried before. In order to get them more immersed in poetry, I've been reading free-verse poems randomly. After I read it, we sometimes discuss it and sometimes don't. The poem is then available typed up and placed in a prominent pocket in our classroom. If the poem is special to you, you're allowed to take one and tape it in your desk, on your cubby, or on a folder OR take it home or put it in your reading bookshelf. I'm trying to teach them that if you want to write like a poet, you have to live like one. And real poets read other poetry and hang it in places they can see it. Now my kids have poems by Eloise Greenfield, Georgia Heard, Langston Hughes and others hanging from the insides of their desks. SOmetiems when we are in a transition, I'll see their lips moving as they re-read them. How can I fault them? They're budding poets!
I teach first grade poetry in the library so it may be a bit different than what would be done in the regular classroom. Our teachers have so much reading instruction to get through that they just don't have time to cover poetry. THey are overwhelmed with the worksheets they have to get through, unfortunately. We focus on a style or poet per month. I see first grade twice a week for fourty five minutes. I usually use two class periods per month to cover poetry.
I review nursery rhymes and Dr. Seuss, I teach Robert Louis Stevenson, Christina Rossetti, Edward Lear and talk about limericks, Couplets, Shel Silverstein, Douglas Florian, Jack Prelutsky. We also read some books writen in rhyme and always talk about that when we do. Since my school is 100% African-American we also do alot of African American poets mixed in -- we introduce Langston Hughes and they memorize "My People" for the end of school program. Nikki Grimes, Eloise Greenfield, Nikki Giovanni and Joyce Carol Thomas are introduced.
I start with nursery rhymes and Dr. Seuss because most of them are familiar with them.
We then move to more funny poems. That way we build upon what they like.
Robert Louis Stevenson and Christina Rossetti are introduced as classic poets. We use a Child's Garden of Verses and many of Rossetti's nature poems.
We finish our year with Langston Hughes -- Visiting Langston is a picture book written in verse about Hughes and is what we use to introduce him to our students. They memorize "My People" They get more in depth in later years at our school.
As for writing poetry, we try writing couplets and stick to that at the first grade level.
Hope that helps,
Leslie