More tricks for counting growth rings (by the way, the five dollar word for measuring age from tree rings and using it to tell something about the tree and the stand it's part of is "Dendrochronology"):
1) always count at least twice. It's easy to miss something if you're just going, "ring, ring, ring" all day.
2) if you can't quite tell whether something is a separate ring or not, wet it to increase the contrast. I usually just use spit because it's always there, but there is a nasty toxic substance whose name I misremember which will make small rings stand out like a picture developing.
3) Be aware that you are measuring the age at the height where you are measuring; that is, if you have a tree which is open-grown and vigorous, you may need to add a year or two to get to a "true" age, while a tree that is suppressed may have many years of growth below your measurement point. Be ready to account for these differences.
4) On trees with a LOT of rings, the easiest way to keep track of your count is to put a tick mark on every tenth ring with a fine-tip pen, then count the tens after.
5) The "false" growth rings Forestryworks mentioned happen when the seasonal cycle is interrupted. Sometimes a tree will respond to drought by storing its resources and essentially not growing, which looks like no growth ring at all, and other times it will set buds and burst them multiple times in a year, which looks like multiple growth rings. The best way to tell the difference is to be familiar with both species and site, as you can't go back in time to be certain.