I only very occasionally see the queen inside the hive. That's intentional. I try to avoid bothering her and the babies—the eggs and larvae that require a lot of care and warmth to stay alive and develop right. As a result, the bottom couple of hive boxes are more or less her private chambers, as far as I'm concerned, only to be invaded if it looks like there's a serious problem, which I can usually tell just by observing the workers' behavior outside the hive. A hive with a good queen has lots of bees happily flying around it. It especially has a good proportion of bees arriving fully laden with pollen. Pollen is full of proteins and is in high demand by the bee larvae.
A queenless hive will show it, eventually by dwindling down to nothing, but initially by moping. If you've ever had an ant farm, you know what I'm talking about; without a queen, listless bees begin hanging around the entrance, not doing much of anything, looking like sullen, bored teenagers. That is, until I decide to get closer to take a good look—then the sullenness becomes belligerence, with bees seriously trying to sting any body part they can get to.
Because a healthy queen is important, some beekeepers make a point of going in and looking for her, inspecting her handiwork to see if she's laying lots of eggs, and replacing her at the first sign of trouble. However, looking for the queen is a lot like playing “Where's Waldo?” You can usually find her by looking carefully in the center of the hive where the eggs and brood are (not the edges and top where the honey is). It helps to look at arm's length for a half dozen bees in a “daisy” pattern—a circle with their heads all pointing toward the center of it. Look for a larger bee inside the circle that's got a long pointy rear end (the better for backing into a cell to lay an egg in it a thousand times a day). That's the queen.
Those workers in the “daisy” pattern are the queen's ladies in waiting. They groom her and feed her, and lead her to the next piece of empty comb in which to lay eggs. In most ways, the hive's “queen” is really its captive. Her attendants supervise where she is and what she's doing, twenty-four hours a day. They constantly evaluate her as well. If she isn't performing the job well, whether because of illness, injury, or age, the signal goes out through the nursery: “Revolution! Start growing a new queen.” (More about this on page 8, “The Sex Workers.”)
Some beekeepers “cheat” by painting a small dot
of paint on the back of the queen's thorax, color-coded
by year so they can not only find her easily,
but know her age as well. For example, the bee
industry standard is that a queen born in 2011 has
a light gray spot; 2012, yellow; 2013, red; 2014,
green; and 2015, blue, with this color sequence
repeating every five years (since queens rarely survive
more than a few years).