Whenever the next PS Vita firmware update hits, it will come with a new app called PS4 Link to help the two devices communicate. Hopefully, you only have to tap it once to take control over the PS4 and its output for remote control, Remote Play or other features. The need for apps to have those annoying Live Screens is probably my last major gripe about the user interface.
The app will also come to iOS and Android devices, but since the Vita is the only one with buttons, that has a massive advantage for actually playing the games. It should look something like the image below, which is a little too close to Windows 8 for my tastes, but Sony has otherwise done a decent job of making a neutral-looking UI.