The pause key is your friend. I frequently pause when some new development occurs or just to to take stock.

Beyond that, when I deploy, I always arrange my units of a given type (e.g. hastati or phalanx) left to right on the battle field so as to correspond to their ordering in the unit display at the bottom of the screen. That way, I can quickly find a unit I can see from the display is taking fire etc.

I also tend to fight using a fairly rigid initial formation that carries over from battle to battle. For example, a row of spears backed by archers and cavalry with some flankers. Often I just approach to contact in that formation (or if defending just hold until contact) and only really micro manage the flankers and the reserve. That approach requires a fairly solid front line (Romans or phalanxes) with lighter troops (e.g. horse archers), you'd have to micromanage more.

More generally, it helps to have an assignment of units to targets, so you know what the function of each type of unit is going to be. For example, in Rome Total Realism, I might assign missiles to target unarmoured stuff (e.g. peltasts, other missiles); heavy infantry to hold the line; cavalry to charge committed enemy in the rear etc.

All that said, I do often get a unit mangled because I lost track of it and, for example, it pursues out of line and gets surrounded. But from a realism point of view, such mess-ups are rather historical.