If you bought a DSLR because you want great image quality, or a higher preforming camera, take into account that the camera only captures what you put in front of it - starting with the LENS. If you have a garbage lens on a $40,000 body, you will have a garbage image. If you put a great lens on an old el-cheap-o DSLR that is possibly a decade old, chances are that you will have the potential to create a great image.
|Nikon 70-200mm f/2.8 (constant aperture) $2,400|
|Nikon 35mm f/1.8 Prime Lens $185ish|
For a cheap starter lens that is a tank and work horse, check out a 50mm f/1.8, or a 35mm f/1.8. All major brands have these lenses at the same, or a similar focal length. They sell new between $125-$225 and give you the ability to make amazing images (if you learn how to use them).
If you now realize your lens isn't going to do what you wanted - sell it and buy the right lens. This hurts, but unless you are doing studio work with big lights while running a constant aperture that is small enough to void out the variability caused by changing the lens's barrel length, then you need the right piece of equipment.
|Nikon 50mm f/1.8 Prime Lens $125ish|
Unfortunately 98% of the time the "kit" lens that is included with an entry level DSLR is not what you want. I recommend buying a used DSLR, and a new lens. DSLRs are tanks - and so are decent lenses. It is entirely possible to create a fantastic portrait kit for under $500 with a used camera and new lens.
STOP SHOOTING IN AUTOMATIC MODE. Here is where all that aperture and f-stop talk comes in handy. Stop shooting in automatic mode. Just because you bought a DSLR doesn't mean that it will make the images amazing for you. In automatic mode you now have a glorified point and shoot. Start shooting in Aperture Priority Mode. In this mode, the camera puts the priority on the aperture of your choosing. This is where that lens info comes into play. Now that you have a good lens, you can start to figure out what the f-stop does. Using a smaller f-stop number creates a "blurrier" background, and a higher f-stop creates a sharper background. I could go into lots of details as to why, but for now thats all you need to know. Aperture Priority Mode is different than Manual because your camera will still decide on an exposure for you - it just holds the f-stop where you want it. This is a step in the right direction!
In Aperture Priority Mode, the camera will keep the f-stop at whatever you set it to (unless you have a zoom lens with a variable aperture - then the camera can't hold it at the smallest number when you zoom). Now when you want to be creative with blurring your foregrounds and backgrounds you can! By adjusting the f-stop number you will find out how much creative control you now have.
In Automatic mode, the camera decides the f-stop for you - which takes away nearly all of your creative freedom, and certainly stops you from choosing blurriness in the foreground and background!