So the classic discussion, how, when, why, etc about splitting a beehive.
There are a few different ways to do a split, so I'll try to put them into a group that makes sense. I apologize if I use a term that doesn't jive with what someone else says, so let's just focus on the logic and methods.
First of all, why. Why split? Either to grow your numbers, or prevent swarming, which, I guess splitting to prevent swarming also grows your numbers, so that's rather moot. But the point being, someone wanting to grow hive count may split a large colony 3-4 ways. Someone looking to prevent swarms may only split it in half. If you want to prevent swarm but also keep low hive count, you can always recombine colonies later.
When to split? Depends on the type of split. Spring time when resources are plenty and weather is good, you can pretty well do any split and for the most part nature will take care of things for you. Winter of course you can't because you can't get a replacement queen. Let's keep it simple and just say split in spring/summer. Just know that the later a split happens, the more you may need to aid that colony to get built up for winter.
Ok, how? First an assumption. Let's assume you have a hive that is double deep 10 frame carried through winter. No mediums to worry about. And let's assume the boxes have a balance of resources within.
Walk Away (Queenless) Split - This is my favorite and absolutely the easiest. Grab a spare bottom board and cover. Take the upper hive body and place it on the new bottom board and place on the cover. Just make sure each box has eggs. Whichever hive does not have a queen will raise a new one. Move the split across your yard, or some folks like to go 3 miles away. This is to retain foragers. If you move locally, you will have foragers go to the old location. That will make the split low on foragers, but they should bounce back just fine.
In 3 days, check the hives again. Whichever one has queen cells does not have a queen. At this point, if you have a mated queen, tear down the cells and put her in in a release cage with candy plug. Done! If you don't have the spare queen, then you were done when you walked away on day one. Check back in 2 weeks for sign that the new queen has emerged and then another 2 weeks to look for eggs. Don't sweat in between. Often times a hive may appear queenless when really they have a virgin or newly mated queen that just hasn't started laying yet.
Queen-right Split - Now in this case you have a mated caged queen on hand the day of the split. This is probably the best way to split as it's the lowest impact on the bees. Now to prepare for this, if you're clever you will prepare. At least 3 days prior to splitting, put a queen excluder between your boxes. Then when you go to split, the box with eggs has the queen. That saves you the otherwise necessary effort of finding the queen. Take the box without eggs and set on your new bottom board, introduce the caged queen and set across the yard. Done!
Now of course beyond all this you may want to super each split or whatever, but that's up to you to decide based on the strength of your split at the time.
What I normally do is sporadic version of the queenless split. I will inspect the hive, and if I decide to split will do it right then. I will dig through to find the queen and cage her so I know where she is at. Then I will split the hive, but will give more resources to the hive I intend to move across the yard. That's because they will lose foragers and will need more food on hand. I also like to take the queen to this hive and leave the old colony in place with eggs. I call this a proactive swarm. The idea is that the split you take away realizes they have a queen but lesser population so they figure they have swarmed. The colony you left behind recognizes a lesser population, and the need for a queen, so they figure the old queen swarmed out. This works best if you actually find swarm queen cells and truly do split them before they swarm on their own.
I always make my splits right there in the back yard and move the split only about 50' away. So I know I'll lose foragers back to original location. To compensate I may shake bees from old location to new a few days later to help balance population back out, but it's not all that critical from what I've found.
The biggest concern I have found in the gulf coast is splitting too aggressively and overwhelming the bees. This can result in loss due to small hive beetle.
Long story short, splitting is very simple in theory and action. Some very basic advance planning can save a lot of headache and effort the day of the split. Have fun with it!