Pretty easy I have to say. One of the cooler features that the PlayStation 4 has is the ability to remotely play your game on a PlayStation Vita. The Vita acts as a thin client to the PS4 and will allow you continue your game on the portable system.
Just go to your Vita and click on a few icons taking you to your paired PS4. After a handshaking routine, you're off and gaming. The video does say the connection sequence is shortened, so expect it to take a little more than a few seconds.
Performance should be good inside the house, but outside, you're going to be subjected to many variables that can affect game performance. I've done game streaming from my PC to my tablet and Android phone and this is how my experience went: minor lag inside the house with OK to unplayable when away.
I have to admit, this is the main reason I'm tempted to pick up a Vita.