If you want to write poetry it's probably best if you don't start by thinking of it as a career. Very few poets make enough to live on; even well known poets often have to do other work too.
However, it is possible to make some money. One way to start is to have a blog or website where you publish some poems to get an idea of public reaction; you can then have a look for some magazines or other publications that produce the type of poetry you write and send them a selection (about 6-10 is a good number). Keep an eye open for poetry competitions too, including local ones, and look at things like your local newspaper or community magazine - they sometimes make a payment for writers, and even if they don't it will be good to get something in print to start you off.
If you have enough work ready, you could always go along to a local venue - a club, pub or even bookshop - that does poetry readings and offer to do one. With self-publishing much cheaper these days, if you manage to make a book of your poems you could sell some copies after giving a reading.
There are other ways to make money such as writing greeting cards or other commissioned work - you may find some ideas here.