I think the cool thing these days is to get those photos with the background "blurred out." First off, the best way to do it with your iPhone is probably to get as close to the face of the person whose photo you're taking, focus on their face, and snap it. On your DSLR, though, there's a couple of more steps, but it's still pretty simple. First thing you've gotta do is set your camera to Aperture Priority (usually an "A" or "Av" on the mode wheel), then set your camera to "single point focus" (you should find this pretty easily in the quick menu). The next part is key: fiddle with the thumb wheel until you've got the lowest possible F number (also called "F-stop") and the lowest exposure time. Then, and this part should be obvious, but I've seen people who aren't aware of it, make sure your point of focus (usually a little red dot you see when you look through the view finder) is on the object you want to appear in focus.
This is called minimizing the depth of field. In other words, you're minimizing the range of distance at which objects appear in focus. I've taken and noted a couple of photos here to demonstrate.
Oh ya, I finally got a lens hood for my 18-55mm lens that works well. I had one of those stupid "tulip" lens hoods, but at low focal length you could actually see it in the photos leaving these hideous black area around the edges of the photos. The new one I got is a bayonet lens good similar to this one (actually, I think that's the one but I got it for a couple of bucks cheaper). It works like a charm.