Open the camera app and switch it to video mode if not already there. Tap the gear icon in lower left corner. In the settings, look for the resolution option. When the submenu opens choose 1920x1080.
Start filming video in 1080p. I would make sure you have a fast enough memory card if you are using one, a class 6 or higher would be best, as the data rates are much higher. Less, if any, slight pauses while recording that can happen with lower class SD cards.
Also, if you are using internal memory, keep an eye on it, as the 1080p video can take up space quickly, depending on the length of your videos.