To write poetry, all you have to do is write poetry. There is a lot of snobbery in the poetry world, as there is everywhere, but writing is one of the best methods I have ever found for getting feelings out. I think it's important to get beyond the idea of writing poetry, and writing well, and just write. Write every day and just keep writing. You have to write all of the garbage before you can get to anything good anyway. I think if you go at writing for the want to write, the want to get your feelings and ideas on paper, you'll do great. Start writing now, decide what you want to do with it later. If you love it, then you can work on developing your craft, or deciding if you want to edit your work, or develop it. There's a great book about writing---very funny and really takes the pressure off called Bird by Bird by Anne Lamott.
In answer to your other questions: no, poems don't have to rhyme, and it all depends on the poem whether or not the rhyming improves it or hurts it.
Also, what do you mean by saying that you tried drawing and failed? There is no failing in any art---not poetry and not drawing. There is only making. If you like making the art or writing the poetry, then keep doing it. It's important to toss out the inner critic and just let your heart sing into the process of creating.