What Davydd said, with the addition of:DIFFUSE NATURAL LIGHT
Diffuse natural light is best, like what you get on an overcast day. This is my No. 1 tip to anyone, and you'll see it come up again and again in discussions of food photography. It's not as harsh as direct sunlight and leads to softer contrast and less severe shadows. So if you can, move the pizza out of direct sunlight. (On that note, make sure the pizza is either fully in a beam of light or fully out of it. The worst is if you have half in direct sunlight and half in shadow. It really screws up the camera's exposure.)SINGLE SOURCE OF LIGHTING
If you're at home and/or can control the lighting, make sure it's all from one type of light source. That is, if you've got some nice daylight coming in from your kitchen/dining room window, make sure there are no artificial lights on. That helps with the phone's auto white balance so it's not trying to account for two different temperatures of light. SHOOT FROM ABOVE
I like to take photos from directly above. Smartphones don't have the kind of lenses that give you shallow depth of field — that effect where the background is out of focus but the subject is clear. They pretty much capture everything in good-enough focus that the background can become a distraction. If you shoot from directly above, you eliminate a "noisy" background and have only the pizzza and the table (see first attached photo).
As Davydd mentioned, you want to shoot from a good distance away. One, because the phone doesn't do well up close but also because the closer you are, the more chance you have in introducing your own shadow into the shot. I shoot from about 2 feet up and then "zoom in" by cropping the photo later.USE NEGATIVE SPACE
If you can't shoot from above (say you're doing undercarriage or crumb shots) try to use negative space or darkness (or even whiteness). I'll hold the pizza up so that a section of blank wall is behind it (attachment 2) rather than a section with our decorations on it. Attachment 3 shows how I used the negative space of a black background (conveniently the bench back in the restaurant I was in) to keep the focus on the rim of the pizza. All the pics here are iPhone — with some editing.EDITING and APPS
I'll probably echo what others before me have said. Here is my workflow:
Shooting: I use Camera+ SOLELY for its "stabilizer" feature. As someone mentioned, it waits for the camera to be in focus AND you to be reasonably still before firing the shutter. Guaranteed in-focus shots. Though I find that the latest version of the iPhone camera (I'm using a 5s) seems to do something similar now. Camera+ might be like $1.99 but to me it was TOTALLY WORTH IT.
First editing pass: Snapseed
(free). AMAZING app. You can sharpen the pic, crop, rotate it, straighten it, adjust white balance, contrast, SO MANY THINGS. I try to keep as true to the original colors as possible, so I rarely use the saturation adjustment.
If needed, I'll use an app called Retouch,
which is MAGICAL. It basically erases stuff like crumbs, spots, a water ring, etc. Again, I rarely use it, because I believe in showing things as is, but sometimes for things like a distracting stain or splotch of sauce on the table, I'll clone that out. It costs maybe $1.99 (I don't remember) but again, WORTH IT, to me at least.Big Lens:
I have never used this for pizza photos because it crosses the line too much for me, but it allows you to blur the background to get an SLR-camera effect with shallow depth of field. The only problem with this is that if you're impatient (it takes a lot of screen-rubbing to use this app) and do it quickly, it can look pretty artificial to an observant eye.
Once I'm done, I post up to my Instagram account(s), my Facebook, Twitter, and Flickr (which I use pretty much for backup/archiving these days). If you're interested in examples, here is my personal Instagram, which has a bunch of pizza and food pics in general: http://instagram.com/akuban
LAST, I will say that it is perfectly possible to take GREAT photos with the iPhone (or other smartphones) these days. When I worked as a food-writer and had to shoot pictures of pizza and other foods, I evolved from using crappy point-and-shoots to nice PnS's to, finally, fancy DSLRs. At this point I NEVER carry my DSLR. It's just too bulky and conspicuous — with the right lighting, angles, and tricks, the phone can do very respectable work.
Good luck, axbman, and if you post these up somewhere, please share the link!