How do you apply for Obamacare?

To answer this question, we would have to know whether you have insurance from your job; if your employer provides it, that will not change. Or if you are under 26 and your parents have insurance, you can now remain on their policy. Otherwise, there are a number of ways to find out which plans you are eligible for. I enclose the link to the official government website, which will explain the law and tell you how to sign up for health insurance.

Also, note that "Obamacare" is not an insurance plan of some sorts. It is an insurance regulatory framework, specifying how and where people can obtain privately-run health insurance, and it also expands existing government-run Medicaid programs to allow more people to qualify. You don't "apply" for Obamacare. You go out any apply for a government program (if you meet the qualifications) at your local Welfare office, or you get insurance through your employer, or you buy insurance through a state (or federal) Exchange system. None of these is "Obamacare" in the sense of it directly providing healthcare coverage.