1. Know that editors need good poems; your good work will be welcome once it finds the right journal for its "home."
2. Create a game that gives you pleasure. Mine is the license plate game. For fifteen years I've been working on getting a poem published in each of our fifty states. More recently, I have been trying to add countries and languages as well. It makes me happy that my poems are in Slovenian even if I can't comment on the quality of the translation.
3. What journals do you love to read? That might be a good place to place your work - even if it takes several tries. I once heard the poet Robin Becker say that it took her more than a decade of sending to American Poetry Review to get published there. Every year one submission went out to them and eventually they published her. Now I see her poems there frequently.
4. Keep query letters short and sweet. Choose one or two relevant things to say and then let your poems speak for themselves. I also include a brief bio so that if the editor wants the poems, they already have it there. The whole shebang goes on a page - or 2/3 of a page.
5. Send local and global. Don't ignore the journals in your area of the country. Most poets and poetry are known regionally.
6. I would strongly advise against paying to have anyone read your poems for a journal (unless it is a contest with advertised prize money). The one exception is some journals now ask you to send on-line rather than through the mail. Meridian, for example, asks a $2.00 fee for paper, printing, etc. That makes sense to me as sending via the postal service cost close to that.
7. The number of poems you may want to send varies although 3-5 poems is a good general rule. You can always check this and other details by looking at the journal's website. If the site hasn't been updated in two or three years, I'd wonder how long it will take for you to get poems back...
8. I have my favorite journals; places, I believe that treat poets well. Starting out I had kind editors at Alaska Quarterly Review, Southern Poetry Review, and Comstock Review. I would still recommend these places to send your work.
9. Talk to other poets and see where they send work. It doesn't hurt to say, "my friend, poet XYZ, thought you might like these poems." I took a poetry class in Boston years ago where we would all pass around a list of where we had been published, then if there was a journal we wanted to send to we would mention the other student's name. In this way we developed a sort of "old boy" network of our own - "young girl network" was more like it.
10. Enjoy the process. Don't let it mean too much when a poem comes back. I think, on average, my work needs to go out about six or seven times before it finds a home - depending on the poem, where I am sending, etc. Celebrate successes and find a poetry buddy to share news with - the good, the bad, and the Ripley's Believe it or Not.