Q: How long will it take to hear back from editors after I submit?
A: Short answer: it depends. Some markets pride themselves on accepting or rejecting submissions on a lightning-fast timetable (a week or less); these are, however, outliers. 3-6 months is a more typical turnaround time, and some journals take up to a year to respond. Many journals include response time estimates in their submission guidelines. Always check these before following up on a submission. If a journal says it typically responds within four months, it won't do you any good to follow up two weeks after submission (chances are, you'll just irritate the editor).
Q: Will I be paid for my poems?
A: Some journals pay for accepted poems; poet Trish Hopkinson maintains a list of paying markets here. However, most journals don't pay authors in cash. Contests are the important exception here--most poetry contests include a cash prize for winners.
Q: Will I keep the copyright to my poems when I publish them?
A: Yes. Poets & Writers has published an exhaustive list of the types of rights that apply to creative writing. There's also a good overview of copyright for writers here (thanks to reader Anna for the tip!). When publishing poems in journals, you will usually grant the journal first serial rights. These give the journal the right to publish your work before anyone else; after publication, the rights revert to the author.
Q: Will I see proofs before my poems are published?
A: Ideally, yes.
Q: If I publish a poem in a print journal, will I get a copy of the issue in which my poem appears?
A: You should. This is a standard expectation; many journals pay poets in 1-2 author copies rather than cash.
Q: How long will it take me to find a publisher for my poems?
A: All together now: it depends! There are no guarantees in this business, unfortunately. The best way to publish poems is to do everything you can to swing the numbers in your favor: submit frequently, brush off rejection, submit again. Most creative writers (especially at the beginnings of our careers) receive many, many, many more rejections than acceptances. The key is to refuse to take rejection personally--and to persist through it.