It also recommends a wired connection for both your PS4 and your computer. Of course, everything is speed dependent and Sony does advise a minimum of 5Mbps for your PS4 to stay stable. The controller still functions as normal and there's pleasantly no need for any button replacements like the PS Vita. Once you're logged in, you can make the above window full screen and you're good to go. The Remote Play app will then hunt for your PS4 and connect.
Finally, plug your DualShock 4 into your PC or Mac using your USB cable and get started.