You have a strong hive that has started to make swarm cells, and you want to make a split.  It is very important that you perform the following *before* the swarm cells are capped.  Once capped, the girls have made up their mind to leave, and there’s no talking them out of it.
Stuff you need:
Qty 1:  Double Screen Board
Qty 1:  Medium super with frames – new, drawn, whatever.
Qty 1:  Medium super, Empty, to be used to hold stuff.
Qty 1:  Duct tape.  Should be in your kit anyway.
Qty 1:  Appropriate summer beekeeping beer.  Pilsner, Lager, etc as appropriate.  I suggest Curious Traveler Shandy. We’l call this Beer A.
Step 1:   Find the queen.  Put the frame that she’s on into the empty super you have.  We’ll call this Box A.  *take your time* — this is really important.
Step 2:  Dump all of the frames out of your super-full-of-frames and set it near your hive.  We’ll call this Box B  Sit this box on top of the double screen board (“DSB”) with the entrance facing up.  You want the DSB entrance to connect to the empty  box on top, not the hives below.
Step 3:  Go through each and every frame in the parent hive.  If there is a swarm cell on it, put it into Box B.  If the frame has no swarm cells on it, but has eggs or larvae, shake all the bees from this frame into Box B, then return to parent.
Step 4:  Do it again.  It’s very important that you did not leave any swarm cells at all in the parent hive.
At this time of the year, you’ll probably have five or six frames with swarm cells in Box B.  Fill it up with frames of pollen and honey (try for a 50:50 mix as best you can) taken from the parent hive.
Return the queen, that you’ve tucked away in Box A, to the parent hive.  Fill in the empty spaces with the extra frames that you dumped out of Box B.
Carefully move the Double Screen Board and Box B AS A SINGLE UNIT – use duct tape to hold things together if you must – and sit it on top of the parent hive.  The entrance should face in the opposite direction — this is very important.
Take the original inner cover and outer cover and use them to close things up.  Your hive should look something like this, from the bottom up…
Bottom Board || Parent Hive Super 1 || Parent Hive Super 2 (and so on) || Double Screen Board with Entrance on the top || Box B || Inner Cover || Outer Cover
Celebrate your successful split by drinking Beer A.
If there isn’t much honey in Box B, you might want to give them a feeder with some syrup, or a candy board.  Same story re: pollen.  Use your judgement.
Consult the queen rearing calendar to get a feel for when the new queen in Box B will emerge, mate, and begin laying.  I give it three weeks before I check.  Be patient.
Let me know if you have questions.
PS:  You’re probably thinking, “my god Eric, I shook all the bees into the new hive!  That’s terrible!”  Don’t worry — all of the field bees will return to the parent.