First, look at the frames, and pull out the
frames with the most bees between them.
If you don't find the queen on those two frames,
you must then engage in some counter-intuitive
thinking, and pick the least likely place a
queen would be. This is a very "zen" sort of
thing, based on the evidence that many people
spend long periods searching for queens in a
straightforward rational manner, only to find the
queen in a very unexpected place after a long
and tedious search.
After you become experienced at this approach,
you have to reconsider the "least likely place",
as you will be finding queens in these "unlikely"
places, thus making those places "likely".
So, you will have to look in even more
unlikely places to be able to find the queen
quickly.
Some say that the beekeeper's choice of "unlikely"
versus "likely" places can't possibly have an
effect on the actual location of the queen, but
these people are dead wrong. They clearly have
never heard of the semi-famous "Heisenberg
Uncertainty Principle", which states that the
act of merely looking at an electron can make it
actually be somewhere else, and even
make it change direction or velocity.
Clearly, the act of looking for a queen can make
her run, change position, and change velocity if
she is moving, so quantum principles DO apply to
finding queens.
If you look in enough hives for enough years,
at some point, you will find so many queens
in so many unlikely places that the day will
come when you don't even have to even leave
the kitchen to find all the queens in an
entire yard of hives. (It may sound unlikely
now, but you just wait until you do it for a
while.)