As you would an expensive camera, take some time to get to know your phone camera. Learn about all the different settings and how to adjust things. Don't just go to straight shooting, find out what you like using most about the phone and build on that.
Set up your photos properly
Just cos it's a phone doesn't mean you should just point and shoot. Take some time do it properly. Make sure its focused, nobody likes blurry photos. Get the lighting right and find a good backdrop just as you would a photo with a camera. A few tips, take photos from the side not aerial as it adds depth of field and don't always shoot against a white backdrop as that's just boring!
No pictures are perfect and nearly all require a little bit of editing. There are some great apps that are free on Android and iPhone. I use VSCO Cam primarily as you can do pretty much everything to make the photo better and it has some great filters too. Another great app for editing skin tone, pimples and red eye is PhotoWonder though don't stick with the presets or they can make you look plastic! I use Instagram a lot too, a little known tool is Tilt Shift, which is the traditional focal blur that you can get on camera's, it means that the focus is solely on the subject so nothing else distracts.
Obviously I'm not saying that you shouldn't own a DSLR, they are beautiful creations, this was just to help you along if you only have a phone at your disposal.
Do you have any tips to add?