What information can be gleaned by visual inspection of a set of tires on a car? How would I interpret excessive wear on the outside edge of the tires vs. wear on the inside vs. wear in the center? What if tires wear differently on one side or one axle?
Tire condition can be interpreted in several ways, visually being the most prominent. Usually excessive tread wear can be seen quite easily using the famous penny test (using an old penny, one where Lincoln's head doesn't overlap the outside edge of the coin).
If part of Lincoln's head is covered by the tread, the tire has a legal amount of tread.
If your wheels are out of alignment due to camber, the depth of the tread will vary across the width of the tire. If you're out of alignment due to toeing, wear will be even across the tire and will be harder to detect. If your camber is off (angle of the tire relative to the road), it might be due to weak springs and shocks, depending on the type of suspension you have. This is where you might see a difference in wear depending on whether you're looking at the front or rear axle. If you push down on one end of your vehicle and it doesn't spring back up and stay (it bounces up and down for a couple seconds), it's probably time for new springs and/or shock absorbers.
If tread wear seems to be occurring in the middle of the tire, chances are your tires are overinflated. Too much air pressure will cause the tire to expand into more of a bicycle tire shape and cause it to wear faster in the middle. On the contrary, tire wear on the outer edges is due to tires being under-inflated, causing the center to retreat further towards the center of the wheel and the edges having more contact with the road surface.
Tire wear can sometimes be gauged by sound or feel. Sometimes your car will vibrate slightly and the tires will emit an undulating sound due to cupping of the tire. If you've ever slammed on your brakes and skidded you might get a similar effect due to a flat-spot on the tire.
Some general guidelines would bee to rotate your tires every other oil change. If your vehicle is pulling to one direction have an alignment done. Don't drive winter tires in the summer. Conduct the penny test when you rotate your tires, and keep in mind the estimated life of the tires (whether they are 50,000 or 100,000 mile tires, etc.).
In addition to the above, any obvious signs of wear should be addressed immediately: If on any area of the tire there is exposed steel or nylon wire, you've worn them down dangerously far and they should be replaced. Punctures can usually be mended depending on their size and location. If your valve stems are cracked or aging they should be replaced to avoid an inconveniently flat tire.
Most tire shops will do inspections on the cheap, so never hesitate to have them checked out if you're not sure about the condition.