I'm going to let someone with more specific knowledge step in, but I think it's worth noting that not every emperor led armies into battle. For example, Antoninus Pius (r. 138-161 AD) never set foot outside the Italian peninsula during his reign. Instead, he appointed governors and generals and would manage the empire by maintaining correspondence with them and publishing edicts, rather than taking a direct hand in accomplishing specific tasks.

The only times you would really get emperors leading armies into battle were times of crisis (such as the Crisis of the Third Century and the decline of the empire). Emperors were much more likely to make official visits to provinces in peacetime or arrive in a war zone after the completion of hostilities. For example, Claudius (r. 41-54 AD) arrived in Britain with reinforcements after his generals had completed their initial conquests and departed from the island shortly afterwards.

Think about it this way, how well could he even run the empire from Rome? There were regional governors throughout the empire that did most of the governing. Though Rome had little formal bureaucracy, the army stationed in the territories often acted like one, fulfilling many normal government functions.

Also you might want to check out the Eastern Roman theme system (http://en.wikipedia.org/wiki/Theme_(Byzantine_district)), which I don't know as much about but is how governance was done in the Eastern Roman Empire.

So, one thing that needs to be realized is that the vast majority of Roman Emperors didn't lead their armies. Augustus added more territory to the Empire than any would, mostly from the city of Rime. Titus, future emperor but at the time simply a general, was marked out because of his "Alexandrian" way of leading the troops from the front during the Jewish Wars. While Vespasian, also future emperor and the father of Titus, took a more "Julian" role being more focused on strategy as mentioned in Josephus' account of the Jewish wars. Of those Emperor's who did rule the empire from afield, I think a passage of Cassius Dio sums it up the best, speaking of Marcus Aurelius

"But the Emperor, as often as he had time away from war, gave judgement. He ordered that much time be allocated to the water clock...so that a just result could be reached by any possible means"

It really, really, depends on what part of Roman history you are talking about, but a general and broad answer is "bureaucracy." If you want to narrow the question down to a more specific period, I might be able to answer, but especially in the 4th and 5th century there was a growing and significant Roman bureaucracy that provided continuity between the various emperors' reigns.

Check out The History of Rome podcast, it's good stuff.