The general answer is very low. Low-ranking officers earned between 125-175 Rubles per year. To put that pay in perspective, prices for an officer uniform, which an officer had to pay for himself, ran around 200 Rubles. Of course, the pay scales increased higher up the chain of command, generals could expect 1300 Rubles per annum and specialized formations like cavalry, Guards, or artillery also received slightly more on average than a standard line regiment. Pay for the enlisted ranks was also incredibly low and far behind their counterparts in other armies.
But the Russian Army of the Napoleonic period was as much a byproduct of its social milieu and the low pay only tells part of the story of life in the Army. Officers were largely drawn from the Empire's nobility, so they did have a degree of independent financial assets. However, an overwhelming majority (ca. 77% in 1812) were from an impoverished nobility and did not own any property. They could have been second or third sons or hailed from a noble family that had seen better days. Military service though offered the promise of increased status. Although already entitled, young officers could hope to rise up the officer ranks and receive a higher noble status and equivalent estate. As with many militaries in this period, such dreams of upward mobility were more prevalent in fiction than reality, but this was one myth that held a degree of power. Moreover, the military was also a way for non-Russian noble to get their foot in the door for state service and establish a familial dynasty of Romanov servitors. The Lieven family, for example, was a Baltic German family that managed to carve out a niche for itself in the Romanov state apparatus starting in the eighteenth century and lasting until the Empire's end in 1917. Military service was one of the ways the Lievens managed to demonstrate their loyalty to the Romanovs and retain a privileged position. The stick to the carrot of a lucky break in the military was that there were few other careers open for the Empire's poorer nobility. The rigid hierarchy of ranks made slipping into commercial estates of the merchantry socially and politically unwise.
The rigid estate system also provided an incentive for the serf-recruits to be more content with their low pay. Entering into the army meant leaving one's soslovie (native estate) and entering into a new soslovie class. The soslovie table of ranks in the eighteenth century was not as hardened and defined as it would become in the nineteenth, but military men, even lowly infantry men, were in a separate social estate set up for military service. This estate status was inheritable and was in evidence in many of the garrison towns that serviced the Russian state. It is important to remember that garrison duty was much more the typical life of a soldier than one of constant battles and garrison life became one of the focal points of a soldier's new life. The children of soldier's wives could enter into garrison schools, first founded in 1721, that fast tracked young boys for military service. Similarly, off duty soldiers were legally allowed to practice a trade and if they were allowed to muster out, often became tradesmen. This estate system imparted to the Russian army a much greater and cohesive institutional character than many of its contemporaries and the long-term service helped add to the Russian military estate as a distinct class in Russian society.
Nonetheless, one of the fracture points in the Russian Army of the Napoleonic period was its low pay. Memoirs from officers almost universally speak of escalating debts and pay being in arrears. Even generals like Prince Bagration found that the income from their new titles and estates could not keep up with expenses. Bagration had to be bailed out of debt from his creditors in 1802 by the state, and even here, his debts still mounted until the War Ministry gave him a furlough of 9000 Rubles in 1811. Not surprisingly, gambling was a universal pastime among the Russian officer corps as it could provide a necessary augment to income. Theft from the regimental coffers was also a danger with the lower ranks and helped add a further incentive to keep the draconian discipline measures in place.
Despite these problems, the system more or less worked during the Napoleonic Wars, Russia was able to field a large, professional army and one which many contemporaries noted had iron discipline. Additionally, while the pay gap between the Russian Army and its contemporaries was quite large, all of the armed forces in the Napoleonic Wars had problems paying its soldiers. The Russian Army may have been more extreme in its parsimonious pay, but such miserliness on the part of the state was the norm for the soldier's life in this period.
Sources
Duffy, Christopher. Russia's Military Way to the West: Origins and Nature of Russian Military Power, 1700-1800. London: Routledge & Kegan Paul, 1981.
Keep, John L. H. Soldiers of the Tsar: Army and Society in Russia, 1462-1874. Oxford: Clarendon Press, 1985.
Mikaberidze, Alexander. The Russian Officer Corps in the Revolutionary and Napoleonic Wars, 1792-1815. New York: Savas Beatie, 2005.
Wirtschafter, Elise Kimerling. From Serf to Russian Soldier. Princeton, N.J.: Princeton University Press, 1990.