It's possible, but rare. If you do make money, it will probably not be enough to live off of, so have another job to pay the bills.
First you need to write and finish whatever you are working on. Then edit, edit some more, edit again, edit eight more times, take a break or two or three, edit again, edit some more, take a few days or weeks or months off, go back and edit again, edit seven more times, break, edit three more times, break, edit, edit, edit five more times, take a couple breaks, edit three more times, edit one final time, edit another time for good luck, take a final break, and edit again.
Then get a current Writer's Market guide and find any and all publishers who match your needs. Write query letters and send them out. Brace yourself for rejections. Do not give up. Even if you are rejected by every single place you send your work, find more and send more query letters out. Just do not give up. Keep in mind that it's much harder to get short stories/poems published than novels, and even novels are hard.