Reading Robert Service's "Spies and Commissars" and though he does a really good job talking about the politics of the people involved, he does little by way of explanations of how the governments actually acted.
Judging from this lack of information about what the Provisional Government actually did during 1917, you'd think all of Russia was an untamed chaos, and the only areas of actual societal organization came from the Soviets in the cities and the Communes in the farmlands where they sprang up. Is this true, or am I missing something? What exactly did the Provisional Government have power over?
The Provisional Government essentially acted as a Parliament of Russia. They could vote on and pass laws as they saw fit, much like a republic. There were two problems however. One, was the problem of the Soviets. The Bolsheviks had set up several Soviets, or workers' councils, to govern from different cities and really weren't interested in following the word and law of the Provisional Government. Even though the PG promised to (and did, to an extent) share power, it wasn't enough, which is connected to the next reason.
Russia was obviously at war when the PG came into power, and in July of 1917, Aleksandr Kerensky, who had taken the reins of leading the PG, called for a renewed offensive against the Central Powers. This was extremely unpopular against the badly beaten Russia, and this emboldened the Bolsheviks against the PG, leading to it's downfall only months later.
To answer your question, it was a republic-like government with the powers to vote on and pass laws that attempted to quell dissent by sharing power with the soviets set up across Russia. However, since Russia was still at war and was torn apart politically on the inside, the PG exercised very little power. The decision to continue fighting a losing war was also not a good call at all.