My advice concerning spreading brood is—“Don’t!” Many beekeepers in the past have attempted to make the queen lay more eggs by inserting empty combs, in the middle of the brood nest. I have done considerable experimenting along this line and in every case the result has been a decrease in brood rearing instead of an increase. The queen has a regular system of her own in the matter of egg laying, and any disruption of her system only seems to confuse her and cause her to slacken egg production. She lays in the comb in a circle and when the brood emerges she goes back and starts over again; but if an empty comb is placed in the center of the brood nest, she lays in it and when she goes to the next comb, instead of it ‘being empty as expected, it may contain brood or honey. Instinct tells her she has caught up with her work, and she therefore takes it easy until the brood emerges. Just as soon as she can, she will get things back to normal. Therefore let the brood nest alone as the bees arrange it, as nearly as you can.
The best time to make increase is at the beginning or Increase during a honey flow. Increase may be made any time during the season, as long as the newly formed colonies have time to build up strong before winter. The later the increase is made, the stronger must it be in bees. Making increase of necessity cuts down the surplus crop of honey. If large increase is desired, no honey crop should be expected; but limited increase may (be made with little interference with the surplus, provided of course, there is a honey crop.
Unless a large increase is desired do not divide strong colonies that have good queens; but rather allow them to make honey. When a large increase is desired, I know of no better way than to take two frames of bees and brood, set them into a new hive and stop up the entrance so no bee can get out. Grass or hay is good for this purpose since it allows some ventilation. If the weather is very warm, shade should be provided.
When forming these nuclei queens should be introduced at the time they are formed. For introducing queens our Push-in Cage gives ideal results. This is used on one of the combs as described later on. The bees should be confined for two days, then the entrance opened to about half an inch. At the same time the cork in the Push-in Cage over the queen excluder should be removed. Two days later the cage can be removed and the queen will go merrily on at egg laying. The best time to make increase is during the month of June when the newly formed colonies will have abundance of time to build up before fall. One colony may be increased to three or four by this method, if there is an abundant honey flow or if they are liberally fed.
Here is the original 1926 page:
Here is a great video that covers brood nest basics:
Check out Honey Bee Brood Diseases to learn more about how to keep your bee brood healthy.