The first element that you will need to consider is the aperture (depth of field or the amount of blur of your background)
Point and shoot cameras generally photograph with small aperture. Meaning they keep most of the what you photograph in focus. This comes in handy when trying to photograph large groups or photos where you want to show off the landscape. On the other hand this is why many point and shoots have difficulty photographing interiors without blur, this small aperture requires lots of light, hence the blinding flash produced by these small cameras.
With an SLR camera it is more about what type of lens you have because that determines the amount of light let into your camera and you can control the blur of a background as well as how much you can keep in focus. The problem when it comes to photographing with a small aperture is that you are allowing less light in your camera so the shutter speed needs to slow down to compensate. The slower the shutter speed the more likely your result will be blurry.
Here are some tips on taking a small aperture photo without blur.
1. Photograph a still object. (moving objects will almost always be blurry)
2. Use a trip-pod or stabilize your camera
3. Photograph in a location with lots of light. (outside is going to yield the best results and the least amount of blur. Naturally the camera lens will have more access to light which means you can use a higher shutter speed)
The second element to consider in setting up your scene. Where is the light. Is the sun overhead and going to produce too harsh of lighting for your photo? Are you going to be photographing into light that will blow out your photo, or make it too dark?
Tips for picking a place to set up your scene.
1. Check out the light first. Ideally you want shade with no sun creeping though. (small amounts of sun will throw off your white balance and your camera will be confused as to whether it should photograph for the darker areas or light areas, so it will over compensate one way or the other)
2. Be aware of the back light (being in the shade and photographing towards the sun) this will create silhouettes of you scene which will be dark.
3. If you are having trouble with blur consider turning on your flash. More light, less blur. Although in an outside setting you shouldn't have issues with blur. And if you can avoid using flash it is always more aesthetically pleasing.
Good luck!
