Get a notebook. Start with the "automatic writing" aka "morning pages" technique, and just write without stopping or editing for three pages. Do that every morning. Then later on, tell yourself "I have to write a poem a day, even if it's the stupidest fucking poem of all time". And then do that. Pick some of them and show them to trusted readers without hope and without despair. (If at all possible, join a writing group.) Listen to what they say. Ask questions about how it comes off. Revise accordingly. I wrote an essay about getting feedback here. This brutal, iterative process is unfortunately the only way to get better at writing poetry.
Here are a collection of suggestions for learning about poetry. Poetry 180 is crash course in modern poems put together by former US Poet Laureate Billy Collins. It's great. If you buy an anthology you'll be confusingly skimming through it for years. Just do this instead.
Sign up for the ModPo course on Coursera through the University of Pennsylvania. It's free. Besides giving you lots of context for modern styles and techniques and big-name poets, the way it teaches you is through videos of a class giving a close read to a famous poem. This will do WONDERS for your ability to close read -- it's really really helpful to watch other people do it and see all the stuff they pick up on. I'm about four weeks into the course, it's great.
Find some journals you like. Check out this post at the top of the poetry subreddit, because besides being a list of places to submit, it's a great survey of contemporary journals. You can also go on Twitter and follow @emptymirror, and they have a great list of lit journals etc. This will get you up to speed on what people are writing right now.
Once you've done all that, which might take like a year, click on this link. It's a collection of scholarly materials which comprise everything in a contemporary MFA program.