I field multiple fleets, for attacking different locations at once on larger games.
Usually, I find that multiple fleets are not usually necessary in small or very small games, other than a few seperate defense forces, and a single assault force.
Otherwise though, I use tactics of feint-attacks, decoys, and side assaults to bring down an enemy.
I play Vasari, so there are lots of techs and ships that give me an advantage to do this.
I usually group my fleets by their designated operation. Capital ships that are useful in hit and run go in one group, carrier groups in another, colonizers in another, control in another, bombers in another, local defense in another, and standard/heavy assault in another.
I usually field multiple fleets of each of these, to give complete control on demand, so as an example I might have 3 groups of standard/heavy assault groups, one or two in each system, ready to defend or attack. I do the same with all the other types as well. I usually group local defense forces immediately, after I have set up shop and moved on, to make defense much easier to control, inted of using the empire-tree.
I find that fighting enemies that use single massive fleets are easy pickings to the multi-fleet setup, like the computer, or many online players.
If a super-fleet charges for one of my planets, I make sure I have enough local defense and Phase-Stabalizers to retreat quickly and backup the local fleets, and with good intel I can see these attacks coming several minutes in advance.
The same goes for assault, I use intel to attack where they are not, and assault places they dont expect me to be. I use Kostra Cannons in a single fleet as well, and micromanage between them to disable defense forces before a raid.
But im a much more seasoned player, and not everyone has the advantage of being almost-crazy when it comes to gameplay speed and paranoia