Healthcare.gov. December the 15th and January the 31st are both listed as deadlines to enroll in or change a 2017 plan. Those who need to sign up are those who do not have insurance through their job, Medicare, Medicaid, CHIP or other.
You create an account on the website and what you pay for your insurance plan depends on your income. In addition, you can apply online, by phone, with in-person help or with a paper application. If you are having difficulties signing up or understanding which plan is best there are people to help you. Give them a call! All US citizens and nationals are eligible to use the marketplace (but you cannot be incarcerated).