How do international PhD students typically obtain health insurance in the United States? Could anyone kindly provide me with information about how PhD international students can be covered by health insurance in the US? : 

Is it often granted by the University? 

How much does it cost, on average (for the student and possibly spouse/children) and what does it cover?

Does "Obamacare" reform affect it anyhow?

I would appreciate any information. Thanks in advance.
This is very university-specific. My university pays the health insurance for students who are appointed to a graduate research assistantship or TA-ship at the half-time (20 hours/week) level. Half-time is the minimum to get the insurance paid, the maximum time allowed for a graduate student to work, and the usual appointment for the vast majority of graduate students. To add a spouse is about $450/mo. I do not know how much children cost to add. The coverage varies all over the map because insurance varies so much by state, institution, and plan in the US. The plan at my institution is for medical care only. Vision and dental are separate and funded entirely by the employee (though they're pretty cheap).

The Affordable Care Act (Obamacare) may have changed this for some institutions which did not provide insurance options to grad students, but mine has for the last 20 years or so, so I don't really know.

All of this information should be on the website of the university you want to attend. You may have to look in the section for employees rather than students, but it's usually there. Look for "benefits" as well as "insurance".