δι᾽ ἀλλήλων συνεστηκέναι: τῇ τε γὰρ τροφῇ τὰ στρατεύματα συνέχεσθαι, καὶ ἐκείνην ἐκ τῶν ὅπλων συλλέγεσθαι

This is a quote from Cassius Dio (42.49.5), who claimed that he was quoting Julius Caesar. Here's a rough translation which I hastily cobbled together for you:

"[Caesar] said that 'It is with maintenance that armies stand together with one another, and that maintenance is collected with weapons.'"

I figured that was a good way to start this off! While Dio was born aboooout 2 centuries after Caesar died, so the attribution itself might just be made up, the point of it is well-made. Armies without a good support behind them cannot operate for any length of time, and the primary reason the armies of Rome were so feared was due to the logistic miracles that Rome was able to produce on a regular basis.

So! Let's start with the Republic, because it came first. And because I'm best with the Republic and such. Starting off, Rome's armies worked in this way for the most part: After Rome's expansion and subsequent division of territory into "provinces," several generals were needed, and those generals were essentially military governors of those regions. In theory, they had ultimate command (imperium) over the army in that province (which extended to imperium over that province). The only little thing hindering that total control? The Senate. The commander had the authourity to buy and requisition supplies, but the Senate had to vote on almost all of the logistics. As Polybius (6.15.2-5) notes:

The consul, when he leaves with his army invested with the powers I mentioned, appears indeed to have absolute authority in all matters necessary for carrying out his purpose; but in fact he requires the support of the people and the senate, and is not able to bring his operations to a conclusion without them. For it is obvious that the legions require constant supplies, and without the consent of the senate, neither corn, clothing, nor pay can be provided; so that the commander's plans come to nothing, if the senate chooses to be deliberately negligent and obstructive.

While this process was usually just a formality - most, if not all, of the Senate was or had been involved in Rome's military at some point in their lives - if the general wasn't politically astute, the Senate could end his campaign before it even started. They voted for the army's pay, they voted for the army's size, they voted how much to give the army from the public treasury to pay for food...the ultimate bureaucracy!

Going down one rank on that ladder, once the Senate had voted, there had to be someone who organized the logistics on less of a macro level - and it wasn't the consul or praetor in charge of the army. That job fell to the quaestor. The quaestor was the first step onto the cursus honorum (lit: Course of honours. It's the Roman political ladder), and it being the first step illustrates how integral the military was for the Roman people. Those quaestors had a rather large number of scribes with them, whose job was to record everything - when and how much soldiers were paid, how much food was used every day, what kinds of food were used, etc etc etc. Being corrupt with state money was kinda difficult in these cases. The scribes would take care of things at a micro level and report to the quaestors. The quaestors would take care of things at a macro level (for the army they were attached to) and report to the consul or praetor so that the general would know what was going on.

Now, you asked about the Marian reforms! How in the world did this work when the generals basically threw their own armies together? Well, luckily for us, Sallust has our backs! Sort of. Anyways, here we go - this is describing the first "Marian" legion, where Marius collected an army of the commons for the first time:

The senate, although it was hostile to [Marius], did not venture to oppose any of his measures; the addition to the legions it was particularly glad to vote, because it was thought that the commons were disinclined to military service and that Marius would thus lose either resources for the war or the devotion of the people. But such a desire of following Marius had seized almost everyone, that the hopes of the senate were disappointed. Each man imagined himself enriched by booty or returning home a victor, along with other visions of the same kind. Marius too had aroused them in no slight degree by a speech of his;

[...] Insert speech here. It's really long, and if you really want to read it (it's Sallust's words, not Marius'), it's section 85 here

He himself in the meantime enrolled soldiers, not according to the classes in the manner of our forefathers, but allowing anyone to volunteer, for the most part the proletariat. Some say that he did this through lack of good men, others because of a desire to curry favour, since that class had given him honour and rank. As a matter of fact, to one who aspires to power the poorest man is the most helpful, since he has no regard for his property, having none, and considers anything honourable for which he receives pay. The result was that Marius set sail for Africa with a considerably greater contingent than had been authorized. A few days later he arrived at Utica, where the army was handed over to him by the second in command, Publius Rutilius. For Metellus had avoided meeting Marius, that he might not see what he had been unable even to hear of with composure.

Now, check out that interesting tidbit. The Senate had indeed authourized him with an army...of a certain size. And money....for that certain size. Marius got more volunteers than anyone had anticipated, and had a few problems as a result. Some historians postulate that that one of the reasons his soldiers were so famed for carrying all of their own stuff on their backs (Marius' Mules) was because they didn't actually have any money to buy donkeys - hell, he was already facing a serious supply shortage before the end of the summer because his army was over budget, and because the Senate controlled all of the grain tributes. You might be starting to see why all of the generals had to be good politicians at the same time ;)

So, what happened if someone decided to be uppity and defy the Senate by...say....requisitioning grain from the province they were in? Well, Livy's 43rd book seems to be almost nothing but discussing asshole Roman generals - here's a quick excerpt :D

A deputation from Abdera arrived in Rome, and stood weeping in the porch of the senate-house and protesting that their town had been stormed and sacked by Hortensius. He had ordered them to supply 100,000 denarii and 50,000 modii of wheat, and they asked for time to send to the consul Hostilius and to Rome. Hardly had they reached the consul when they heard that their town had been taken by storm, their leaders beheaded and the rest of the population sold into slavery. The senate regarded this as a disgraceful proceeding and they made the same decree in the case of the Abderites that they had made the previous year in the case of the Coronaeans, with instructions to the praetor to announce the decree to the Assembly. Two commissioners, C. Sempronius Blaesus and Sextius Julius Caesar, were sent to restore the Abderites to freedom, and to inform Hostilius and Hortensius that the senate considered the attack upon Abdera as utterly unjustifiable, and demanded that search should be made for all who were enslaved in order that they might be set free.

While the Senatorial control over this stuff started breaking down in the Late Republic, and generals began doing things more for themselves, vestiges of that control still tried to exert themselves. If they found it convenient, generals such as Pompey would accept the Senate's help, but you read about generals just doing their own thing to get the money and supplies they needed just as often. Sulla would "request donations" from Greek temples, Caesar would "accept tribute" from the Gallic tribes, etc. The general layout within the army itself still stayed strong, though: The general at the top would be obligated to be at the top of macro-level logistics, while the quaestor actually took care of those things.

And then! Augustus happened. And shockingly, the world did not end.

Augustus' military reforms took place over time, and the longer he maintained his control, the more he was able to centralize his reforms, including that of logistics. As time passed, he ensured that all logistical everything passed straight through him - not the quaestors, not the consuls, but him alone. Augustus' scribes kept all records of finances and foodstuffs for every legion in the field, and all decisions in the field had to be channeled through him. Legates who were appointed to command the armies were considered to be the Imperial voice, and made it so that the ystem wasn't overly clunky, but they answered only to the princeps himself.

Alongside the legate came the procurator a rationibus, who kept track of weapons, forts, payments, salaries, and deductions. This procurator was responsible for compiling, documenting, and presenting these stats to the emperor - something that's not always easy :) A slave called a dispensator would be responsible for actually doling the money out to the legions in question, and, as a result, would be a pretty important person, while another man would be responsible for the other logistics of the army.

Looks like I've run out of space, but I think I covered everything! Feel free to ask any more questions if you've got them! :D