There is one thing that as a DSLR user that you have over a point and shoot. Aperture control. This can be one of the most powerful tools you have to create good looking photographs. The wider the opening (lower the f-stop) the more shallow the depth of field. You can check out a full blog post that I did on aperture if you want to know more. Check it out here
This blog post is about separating your subject from the background. I have three examples below from my recent trip to Cuba. The first one below I used a small aperture to ensure that the city in the background was in focus almost as much as the subject. I was able to get some separation from the background by getting low and shooting up. This puts the horizon just below his chest and his upper body pops off the blue background.
|Overlooking Havana, Cuba|
The next example here I used a larger aperture blurring the background. When you have a person in front of a blurry background there is a sizable amount of separation. Your eyes do not get confused and tend to go directly to the subject.
I saw the door that is in the background and thought that it would make a fantastic backdrop for some portrait work. I positioned the individual about ten feet in front and used a long lens with a wide open aperture. This allowed me to compress and enlarge the background and blur it at the same time, providing excellent separation.