Welcome to Nikonians! Congratulations on your new D5200. You must put the camera in Live View by rotating the Live View switch on the top of the camera below the exposure mode dial.
I would not recommend using Live View to capture images like using a point & shoot camera. Live View is useful for shooting macro subjects, or when manually focusing with the camera on a tripod or when shooting video. For general photography using the viewfinder and proper handholding technique will provide significantly more stability than holding the camera out in front of you like a P&S. The more stable the camera, the sharper the image will be. Once you get used to using the viewfinder it will be second nature.