For trees with determinate growth, the scales of the terminal bud completely encircle the twig. In spring when the terminal buds burst open, the protective scales, which are modified leaves, elongate and even green up. They’ll photosynthesize for a short period of time before the true leaves emerge. Soon after the scales are shed, leaving behind small little bud scale scars that, like the scales, also encircle the twig. The terminal bud scars (sometimes called annual rings) are very easy to see on buds that have lots of small little scales (like on sugar maple and American beech). On species with fewer scales, like striped maple, which has just two scales, the annual rings can be difficult to see.
Note: On indeterminate branches, the last bud on the twig, called a pseudoterminal bud, is really just a lateral bud and the bud scales don’t wrap around the twig.
At this point, it might not be that tough to figure out how to use terminal bud scars to age a twig. Each year the terminal bud bursts open in the spring, the scales are shed, and all that’s left is a ring of bud scale scars. The branch continues to grow and produces a new terminal bud later that summer. The process repeats year after year. Working back from the tip of the branch, the first ring of scars is from the most recent growing season. Each subsequent ring is one year farther back in time. The terminal bud scale scars do get harder and harder to spot as the bark gets thicker, but for many species you can count ~15+ years back in time. This past week, with a group of kids we were able to count 32 years back on a striped maple!