I was wondering mainly about the generals of the republic and early empire. Scipio Africanus and Caesar for example.
Well, that depends on how the battle was going!
/u/DonaldFDraper once said that a Roman General in command of the situation had to quite literally do nothing. Perhaps an oversimplification, but a succint statement none the less.
The infantry that made up each Legion and maniple, and so on and so forth, would more or less be in the hands of the subordinate commanders, a Praetor would only need to see to their mustering and forming of the lines of battle. A Praetor would then give general commands to advance, or hold, to his Legions and it would then be assumed that the well drilled, well trained Roman infantry would carry the day after going through their evolutions and drills.
In theory, at least.
In practicality this passive control of the army often left, especially during the early Republican era, the Consuls or Praetor hopelessly confused when an opposite General exerted some notion of personal control over his army's actions. This is why the great trap at Cannae worked so well; a commanding Praetor would've only noticed his Maniples driving in the Carthaginian center, as they would be expected to do, and nothing else. How could he surmise that Hannibal was personally managing his center and making sure they stretched, but did not break?
I'm loath to use Caesar as an example because we really have no firm evidence if he was, in fact, a 'good' General. He was certainly an experienced campaigner but our main campaign histories of him are written by him, and while written in expert, detached prose, have always been somewhat suspect. I'll use him as an example for how a Roman commander would exert personal influence and 'direct command' over his men.
During his conquest of the Belgae tribes, Caesar's encamped army was attacked strongly by his opponents and a pitched battle resulted. Most accounts (what few there are) of this battle in particular note that while Caesar was wherever he needed to be most visible to his men, giving encouragement and threats as the situation demanded, he never gave but the vaguest of orders (e.g; he did not trod on the Legatus' toes) once he had accomplished drawing up his surprised legions into some semblance of a battle-line. He mentions that in certain cases when he noticed the situation was prime for it, he personally ordered nearby men to throw their pilums, but we can largely discount this as situational and atypical. The Legions, once formed and no longer shaken in spirit, began to push back the Belgae of their own volition and through the commands of their immediate Legatus.
Further interaction in the battle largely deals with Ceaser redeploying currently uncommited legions and giving them generic orders to attack, or re-establish contact with, etc.
Any of this can be read personally in Volume II of the "Bello Gallico", of which many University presses offer free to read online English translations. The Battle in reference is generally called the Battle of the Sabis.
To answer your question, then: A battle for a Roman Praetor would be a rather confusing affair, and require quite a bit of rushing about - if it was not routine. Orders would be mission-oriented, that is, vague, and faith would have to be put in the appointed Legates. Really, as with much Classical combat, the Commander in Chief usually only had direct control over when to commit reserves, order a general advance, retreat, or direct a 'stance' to adopt, if the units were still responsive to it.