A fisheye lens is an ultra-wide angle lens (short focal length) that produces strong visual barrel distortion intended to produce a hemispherical image or a wide panorama. 

1. The main reason to use a fish-eye lens on landscapes is to emphasize the foreground and still allow you to include the sky. Remember, you must have something of interest in the foreground, so move around and select carefully. Lismore Castle, IrelandLismore Castle Ireland from the Blackwater River with reflections.
2. Landscapes with the horizon at the middle: should have little distortion, and will look like a panoramic picture. So if you need a very wide angle landscape (nearly 180 degree view), this may be the perfect lens. Often, however this may be boring, and at times you may want to emphasize the curve of the earth in the image and embrace the distortion but placing the horizon line close to the top or bottom of the frame. However, avoid getting your limbs in the frame. Never forget basic composition so look for leading lines, color, etc. to vitalize your landscape. Gloucester Harbor
3. Use the fish-eye lens to enhance shape or structure in architecture: such as the curve of a building or object. Fish-eye lens will bend and distort verticals so either embrace or avoid or correct this (Tilt shift lens or post processing in LR or PS). 20140619_CAM_051
4. Try using a fish-eye as a vertical image (instead of horizontal by rotating your camera 90 degrees) to be able to include the foreground and more sky. Haleakala Crater
5. Also try pointing directly up at the sky or somewhere in between. In these pictures, the palms and sky take on a completely unexpected look. Full Moon AboveSepia toned skyward view of 3 palm trees and the full moon Palms
6. Move closer to your subject to exaggerate DOF - depth of field (versus a telephoto lens which will flatten it). However, with portrait subjects close to the lens, facial features will become quite distorted. Unless you want this comical effect, avoid getting too close to people. A good use would be to keep people closer to the mid ground to help capture them in their environment or place. Facial Distortion with Fisheye