The concepts of splits are:
You have to make sure that both of the resulting colonies have a queen or the resources to make one (eggs or larvae that just hatched from the egg, drones flying, pollen and honey, plenty of nurse bees).
You have to make sure that both of the resulting colonies get an adequate supply of honey and pollen to feed the brood and themselves.
You have to make sure that you account for drift back to the original site and insure that both resulting colonies have enough population of bees to care for the brood and the hive they have.
The old adage is that you can try to raise more bees or more honey. If you want both, then you can try to maximize honey in the old location and bees in the new split. Otherwise most splits are either a small nuc made up from just enough to get it started, or an even split.
An even split. You take half of everything and divide it up. Face both of new hives at the sides of the old hive so the returning bees aren't sure which one to come back to. In a week or so, swap places to equalize the drift to the one with the queen.
A walk away split. You take a frame of eggs, two frames of emerging brood and two frames of pollen and honey and put them in a 5 frame nuc, shake in some extra nurse bees (making sure you don’t get the queen), put the lid on and walk away. Come back in four weeks and see if the queen is laying.
A typical split. Same as above, but you either introduce a queen you bought or you come back in four days and destroy any queen cells that are capped. These were started from larvae that are too old. Now walk away and let them raise their new queen. If you introduce a queen they will be four weeks ahead of the hive that is raising their own, so you will have to put them in a larger box than a nuc to start with.
A cut down split. This is very timing critical. It should be done shortly before the main honey flow. The purpose is to maximize the foraging population while minimizing swarming and crowding the bees into the supers.. There are variations on this, but basically the idea is to put almost all the open brood, honey and pollen and the queen in a new hive while leaving all the capped brood, some of the honey and a frame of eggs with the old hive with less brood boxes and more supers. The new hive won't swarm because it doesn't have a workforce (which all returns to the old hive). The old hive won't swarm because it doesn't have a queen or any open brood. It will take at least six weeks or more for them to raise a queen and get a decent brood nest going. Meantime, you still get a lot of production (probably a lot MORE production) from the old hive because they are not busy caring for brood. You get the old hive requeened and you get a split. Another variation is to leave the queen with the old hive and take ALL the open brood out. They won't swarm right away because the open brood is gone.