Sunset view from the vantage point at Sun Moon Lake, Taiwan
At the very basic level, the aim of sunset photography is to maximally capture the vivid orange, red and yellow colors produced by the setting sun, as well as show the sun as a tangible ball of fire, as such. This should not be taken to mean that the picture is orange or red-tinted, merely that the colors in that range are emphasized, ideally while still retaining much of the fidelity of the other colors produced or present as is possible. The ability of one's camera or one's own settings to successfully achieve this balance will bring you pictures great contrast such as this following picture.
Sunset view from Sky Bridge at Pinnacle@Duxton, Singapore
See that the top half of the photo is a solid blue, while the effects kick at the bottom half of the picture where the light of the sun is peeking out of the heavy clouds, whereas a simply tinted picture would be stained orange where orange does not belong. This effect can also be used in the rarer occasion where one finds a picturesque object reflecting the light from the setting sun.
Ground-up view of 63 Building from Han River (Han Gang) Park in Seoul, South Korea
A camera would produce the result of the visible shape of a sun by drastically reducing its light intake. This effect conveniently allows the photographer to take silhouette shots in that magical window where the sun is really low and gets really glaring. There must be some skill and artistic creativity involved in positioning the sun, the subject, and the background, because while one need not worry about grain or color, one has to worry in turn about the former three factors, since the slightest misjudgment in positioning could result in the silhouette having funny extra shapes or unwanted background shadows.
Sunset silhouette shots from Han River (Han Gang) Park in Seoul, South Korea
In the case of the last photo, not having a complete silhouette turned out well (to me at least) since the subject is wearing white, and I think having some of that turn up puts an additional bit of depth into the shot. The higher-than-usual light intake allows the sun to look much larger as well.
Of course, one has to play with his or her camera, and I daresay get intimate with it, to know the camera's abilities and limits. Point it everywhere and anywhere when shooting sunset, and observe how the color and light balance changes accordingly. Once you get that, you'll start to understand what kind of shots are within your reach.
Then just go shutter-happy.