Angles and Perspectives
Photographs of people are conventionally taken at about eye level. But if you want something different, you should experiment with taking them from different angles. For example, try taking them from above or below the subject or to the right or left. The subject looking up, down or sideways at the camera also produces some really interesting effects.
Eye Contact
Portrait photographs are usually taken with the subject looking at the camera. You should try being a bit different and have her looking at some object of interest. If you want to be somewhat abstract, have your subject looking outside of the picture, which attracts speculation about what could be so interesting. Or just have her looking at something within the actual portrait.
Change Locations
Think about where you normally take your photos. So you are on holiday and it̵7;s a pretty exotic location. You come home and go through your photographs and realize that you didn̵7;t really capture any feel for where you were. Next time think about the real local culture and try to capture it by getting away from the normal tourist trails. Real people living their real lives can be much more effective than contrived pictures taken in contrived situations.
Lighting
Night scenes can be quite effective ̵1; even stunning if you take them during, say, a fireworks display. But you can also use lighting in your pictures, and the effects can be excellent. For example, you can hint at a darker side of a subject or situation by using dimmed side lights that illuminate one part of the face or object. Or you can use multicolored lights to create some unusual effects. And don̵7;t forget natural lights and shades ̵1; these can produce some of the best "real life" images.