It might sound simplistic to say that what a poet does is write poetry, but this is the essence of the artform. What else a poet may do is highly dependent on a number of factors, like how famous the poet is, whether he or she is professional or amateur, what kind of training the person has, and whether the job of writing poetry is full-time or an augmentation to other work. Poets come from diverse backgrounds, too. A true artist may crouch in a jail cell finding the right words, another could ply his craft in poverty, a few poets snatch a quick moment in between baby’s naps to write down a verse, and yet other artists attend state dinners and appear on Oprah. Education and orientation range from those barely able to spell to those with doctoral degrees.
This comes back to the simple description that the poet writes poetry. Given the opportunities available, such artists may get to perform their work full-time, and might even get paid for it. Poetry is not an extremely popular art form in many places, and getting recognition can be difficult. Artists might begin by submitting their pieces to small poetry magazines, and if they're very lucky, some of the few publishers that recognize poetry could publish a book of their works. Greater recognition could be parlayed into a career.
One easy marriage in poetry is that of poet and academic. Many well-recognized poets teach in language departments and they may especially focus on the teaching of how to write and analyze poetry. From this standpoint, writing poems doesn’t necessarily have to be about profit, but recognition can still advance an academic career or make it easier to publish volumes of work.
Lots of people are good poets without having to be taught. Education can range from secondary to post-secondary work, which may not at all be in the subject of learning how to write poems, but could have been gained in many other ways. As mentioned, a few poets, especially those coming from impoverished backgrounds, may not have very much education at all, but they might gain notice because their words speak in a particularly poignant or gritty way to the state of the world.
It may be that poets who get known, and there are lot of excellent ones that never will, have some quality that touches people who read their work. Many people view poetry as using flowery language that rhymes to convey romantic themes, and they this see as somehow deceptive. Those who love poetry would argue that it is the use of effective language to tell truths about the human condition, and that fantastic poets truly have come from the highest ivory towers and the scariest prison yards.
Ultimately, the writer of poetry chooses language that reflects their ideas or state of mind, and he or she hopes to communicate such thoughts to others. Some people get lucky; they become a Maya Angelou, a Robert Frost or a William Penn Warren. Many other poets will likely remain in obscurity, while still deriving great pleasure from the well-turned phrase.