About Tire wear: There is no real rule of thumb about when a tire is worn out, but you may start to notice some changed in how the tire rides. For instance, I had a rear WTB Velocoraptor that I liked really well (a good mud tire) It had huge paddles with nice sharp edges. As I rode it for a number of years the knobs wore down and the edges rounded, making it a much faster tire and good in loose rock and dirt, but not as good in the mud. In this case I didn't replace it, I just used it differently.
For Road tires you will notice that the rear tire starts to get a flat spot in the center where the tire contacts the road.
Most people don't notice a difference in the ride as this happens, but picky riders may notice a change in the way the tire rides. At this point you would definately not want to move the tire to the front wheel as you would notice the difference in cornering. Many people replace the rear tire when the flat center becomes pronounced, others ride the tire until they see fabric and then discard it. You should note however the thinner the rubber gets, the more prone you are to flats. You may also consider rotating the tires from front to back periodically. This can potentially lengthen the life you will get out of the pair of tires.
Signs that your tire should be replaced:
Knobs falling off (MTB) - If the knobs have actually been ripped off, or are starting to separate from the tire it might be time to replace or at least demote the tire.
Knobs being worn down (MTB)- The knobs will get shorter over time. Once they are flush with the tire in any given place it is a sure sign that the tire needs to go. Usually it doesn't get to this point, you will notice a loss of traction long before you get to that point, and usually have some other structural problem with the tire first.
Visible Fabric (Road or MTB) - If you are seeing fabric where there was once rubber, you should have replaced the tire a while back.
Dry Rot (Road or MTB) - Old tires will start to form cracks in the sidewalls, these cracks when severe will tend to allow your tube to blow out the side of the tire. Destroying the tire and making it terribly difficult to repair mid-ride.
Damage: Usually the reason you will be replacing a tire is due to a cut in the sidewall or sometimes even the tread itself. Look for cuts that have damaged the casing (the fabric). These should probably be replaced, if the spot is raised as if the tube is trying to push through it should definately be replaced. Any time you can see fabric on the tire it is usually time to go.
Metal vs. Plastic tire levers: We highly recomend that you use plastic tire levers rather than metal ones. Once you get good at changing tires, you will find that you use tire levers less and less, but if you must use one, make it plastic. Metal tire levers, while stronger have a high probability of damaging your rim, especially if it is a tough tire or and inexperianced mechanic.
If you forget you tire lever - If you get a flat on a ride and realize that you don't have a tire lever and you can't get the tire off with your bare hands, try using the quick release lever from your wheel. It is obviously not ideal, and you will need to be especially careful not to damage your rim, but it may get you through in a pinch.
