The president signed executive actions today declaring that it is the policy of the United States to "prevent the admission of foreign nationals who intend to exploit United States immigration laws for malevolent purposes."
Quick take: The ban on Syrian refugees entering the U.S. has no end date. Other refugees have a temporary ban. There is a refugee-admission ceiling set at 50,000 for fiscal year 2017. (Note that Obama planned to admit 110,000 for fiscal year 2017.) There are exceptions for religious minorities if they are fleeing religious persecution.
More details below, updated as we go: