Well I split my hive this past March, mostly because they had made queen cells and I was trying to stop them from swarming. It didn't work, as they swarmed anyway. I followed the advice of Michael Bush on how to do the following split.
When I split the hive, I had a full super with frames (I had 10 frames)(can be empty or wax comb) on a bottom board sitting on the ground about 3 feet away from the hive I wanted to split. You can place your new split further away if you want.
Now of course I had a queen cell to transfer into this new hive, which you do not. So you will need to transfer a few frames (could be as little as 2 frames) of brood with eggs. The eggs are very important for your split as the new hive will need to make a queen from the eggs. In addition I transferred 3 frames of pollen and honey into the new hive. So about 5 frames would do it for a 10 frame super.
You will need to make sure you do not transfer the queen into the new box, so you need to know where she is and leave the frame with her safe.
Then I went through the old hive frame, by frame, and shook many bees into the new box. The reason behind this is the nurse bees who have not yet flown, will stay with your new split. While the bees who forage, will fly back into the old box.
When I felt I had enough bees in this new split, I stopped the shaking. That was it, and you have to feed this new hive until they are bringing in enough on their own.
I could not believe how easy it was to do this, and I was very fearful of the whole process, but it worked out great and now I have 2 hives and the new split is very strong.
I am also a new beekeeper and I am sure you will hear from even more experienced beekeepers soon.