I can offer a few tips in the form of questions. This by no means is all encompassing but should give you an idea of where your analysis is heading.
Good poems to look for if you're not too picky are english poems from the WW1 era or Romantics (like Byron). Poe is always fun to write about too...
Find a poem you don't mind reading a few times.
Analytical portion (usually any poem can be analyzed like this. It's all about what the words mean to you, so there are no wrong answers
)
What is the poem about?
What is the poem's purpose?
How does the structure of the poem contribute to its' purpose?
What are some powerful words and how do they make you feel?
How does the rhythm of the poem affect the way it's read?
This bit's tricky at first, but gets fun if you get good at it. I suggest you find a place where it doesn't matter how goofy you look and tap your finger/clap for every syllable, bit of punctuation and end of a line you read. This is a good way to feel the poem's flow (like how good musicians pause or emphasize important words and lines)
Does the poem have a steady repetitive rhythm?
Does the poem ever break rhythm? If so, on what line? what can emphasis on this line mean?
Does the poem's structure suggest anything of it's content?
Biographical portion:
Who wrote this poem?
Why did they write it?
What does this poem say about their personality/life/style?
Sociological:
What was going on in the world when this poem was written?
How does this poem reflect on the world?
Does this poem mean anything to today's society?
Best of luck mate.