This is the "nuc" method of requeening I use in the Fall with excellent
results.  The procedure is adopted from D. Sammataro's "The Beekeeper's
Handbook", pg 83.  She calls it "division screen requeening", and her
description includes diagrams.  Although you will see that a fair amount of
work is involved, the big advantages to this method are the high new queen
acceptance rate, and the low risk of creating a queenless colony.  The method
is perfect for those who keep queens stored in small colonies (nucs)
 
Procedure summary:  A small colony with the new queen is created.  The old
colony is dequeened, and the two colonies united.
 
I'm assuming that most of you keep your bees in two deep brood chambers.  The
method works equally well for folks like me who use 3 Illinois brood
chambers.
 
Special Equipment Needed:
 
1) A double screen.  Make a frame the size of a hive body (19 7/8 X 16 1/4
inches for standard American gear) out of 1/2 X 3/4 molding, then cover both
sides with screen, or better 1/8 mesh hardware cloth.  One will be required
for each hive you do.  You'll find these useful anytime you have to keep bees
from getting into (or out of) a box (just-pulled supers at harvestime,
preventing robbing during hivework, and similar uses).
 
2) A means of providing a bee entrance to the upper hive body.  This can be a
shim with a notch cut in it (preferred), an unplugged hole in the upper hive
body, or even a couple of 3/8" diameter sticks.
 
3) A spare hive body is useful for holding frames during manipulations.
 
Procedure (assuming you're buying a new queen)
 
1)  When your new queen comes, start by locating the existing queen in the
colony to be requeened.   Place this frame with the queen on it aside.  If
the existing queen is not marked, mark her now, preferably a different color
than the one you new queen has.
 
2)  With the queen known to be out of the hive, ensure the top hive body has
at least 2 frames of old capped brood (dark brown cappings), one with
uncapped larvae, and one or two frames of stores.   You will usually find the
upper hive body is already in this happy state.   Some people will shake all
the bees out of the upper hive body; I don't.
 
3)  Place the frame with the old queen on it into the lower hive body.
 
4)  Install the double screen over the lower hive body.  The bees in the
lower body now cannot get to the upper hive body.
 
5)  Install your bee entrance to the upper hive body.  I either use a shim on
top of the screen, or two 3/8" diameter sticks propping up the forward side
of the upper body.
 
6)  Place the upper, queenless, hive body on top of the shim (or whatever).
 
This is what you should have at this point:
 
    The old queen, with most of the bees, will be down in the lower hive
body.
 
    The double screen will prevent bees (especially the old queen) from going
directly from one hive body to the other.  However, warm air will circulate
between the hive bodies.
 
    A flight entrance to the upper hive body has been provided.  The upper
hive body is basically now an independent bee colony, although for the moment
it is queenless.
 
7)  Install your new queen (should be marked) in the upper hive body per the
directions that come with her, and close up the colony.
 
8)  Wait 2-3 weeks
 
9)  Examine the upper colony.  By now the new queen should be out and laying.
 Make sure she is doing well.
 
10a) If you decide to keep the new queen, then go into the lower hive body,
and find and kill the old queen.  Remove the double screen and the shim, then
place a sheet of newspaper on top of the lower body.  Replace the upper body.
  The bees will gnaw through the newspaper, uniting the colonies with the new
queen.
 
10b) If you decide the new queen is no good (it happens), then kill the new
queen, and either try requeening again or unite the two colonies with the old
queen.
 
 
You will note that with this method, you always have at least one accepted
queen (new or old), and you don't get rid of the old queen until the new
queen is accepted.  You also get the bonus of two queens laying for a while.
  I've found the high acceptance rate for the "nuc" requeening method
justifies the work involved.
 
If you keep spare queens in small colonies (nucs), then you can requeen as
follows:
 
1) Take the top and inner cover off the colony to be requeened (main colony).
 
2)  Place your screen and entrance shim on top of the main colony's boxes.
 
3). Place the box with the nuc (with the new queen) over the screen and shim.
 
4)  Leave this alone for 2-3 weeks.
 
5)  Confirm the queen in the nuc is laying properly.
 
6)  Find and remove the old queen from the main hive.
 
7) Unite the colonies via the sheet-of-newspaper method described above.
 
Try it, you won't be sorry.
 
W. G. Miller
Gaithersburg, MD