If you go into your settings file (you can open it with notepad or something to edit it), change this line:
MaxEmpireWindowStackSize 10
This value is normally 10...when the empire tree is "stacked", it will group similar ships and stuff by groups of 10...you can put any number you want, but anything over several hundred should be good enough to select all of a ship type with a single click....that way, you can select all your bombers or all your HCs with one click...
In this manner, telling your ships to attack the appropriate targets (ie what they counter best) is really easy to execute and negates the need for multiple fleets during a single battle...
If you are more concerned about fleets at the macro level (like, where your fleets are on the map), dividing fleets is actually quite risky...that being said, sometimes it is necessary to split your forces (say, to have one reinforce a starbase while another goes on the offensive)...the empire tree is your friend in selecting the appropriate ships needed for each fleet...that being said, what exactly do you mean by dividing fleets?
How you divide fleets is highly dependent on what you want to do with them...flak/support/fighters are great for reinforcing planets while siege/flak/support are great for raiding planets...
