You're very much in luck as there is an excellent source on this topic, a book by none other than Владимир Григорьевич Фёдоров, designer of the Federov Avtomat, often called (incorrectly, in my humble opinion) the first assault-rifle. As it so happens I've translated part of this book for a blog post.

Mr. Federov (The name should actually be written in English as Fyodorov, but I will go with the common mistransliterated Federov) was an arms designer in the early 1900s, and an expert on the matter.

So, on to the main topic at hand. Page 7 of this book presents us with the following table, where the amount of weapons on hand in 1914 is compared with the standards of 1910.

Name of the weapon	Required weapons for troops and reserve	Weapons available with the troops and in reserve in 1914	Surplus (+) and deficit (-) of weapons according to 1910 norms
3-line infantry rifle	3 270 320	3 427 077	+ 156 757
3-line dragoon rifle	464 405	540 272	+ 75 867
3-line Cossack rifle	189 598	204 394	+ 14 796
3-line carbine	286 259	118 657	- 167 602
4.2-line rifle (Berdan)	348 421	362 019	+ 13 598
Total	4 559 003	4 652 419	+ 93 416
Revolvers	436 210	424 434	- 11 776
3-line Maxim machine gun	4900	4157	- 833

To more properly translate the literal names of these weapons here, the 3-line infantry rifle is the long M1891 Mosin (Or Mosin-Nagant, in the West), the dragoon and Cossack variants are shortened rifles, the dragoon capable of mounting a bayonet and the Cossack not being able to. The carbine is the M1907 model. The 4.2-line Berdan rifle was Russia's rifle before the Mosin, but it would remain in use with the massive Russian Army long after it was obsolete. In fact, many saw use during the Russo-Japanese war of 1904-05. The revolvers are presumably both Smith and Wesson Model 3s in .44 Russian and M1895 Nagants in 7.62×38mmR. Finally, the Maxim machine guns are just that, the very same Maxim machine guns that would dominate WWI, chambered for the standard 3-line 7.62×54mmR.

Now, when we look at the numbers here, it's actually not too bad. There are more rifles on hand than necessary, only the carbine is really lacking, which is entirely logical since it is the 1907 model. As a weapon is produced and introduced, all sorts of efficiency in production is realized, the Mosin rifle was 23 years old in 1914, the carbine only 7.

Good, now we have the numbers at the start of the war, but that doesn't necessarily tell us much. Once World War I got going, the Russians would lose massive amounts of weapons.

Although in no way as good of a source as the Russian language source quoted above, the small Osprey book on the Mosin has the following to say:

As a consequence of this poor logistic planning, the Army was short of 870,000 rifles just two months after mobilization. Rifles were lost in the disastrous East Prussia campaign of August– September 1914 more quickly than they could be replaced. The catastrophic losses that occurred at the battles of Tannenberg and the Masurian Lakes simply aggravated what was an endemic problem. This deficiency characterized Russia’s inefficient logistics throughout World War I. The fully mobilized Army needed 5,500,000 rifles. A further 5,000,000 were needed to arm those conscripts called up during the war. Given that the Army lost some 200,000 rifles per month, combat losses over four years, calculated at 200,000 per month for 40 months of war, equated to 8,000,000 rifles, giving a total requirement during the war of 19,500,000 rifles. Russia procured a total of 11,392,000 rifles from all sources, which left a shortfall of no fewer than 8,108,000 rifles.

Although I need to stress the Osprey books aren't the best of sources, I believe they are roughly correct in their assessment here. Indeed, the Russians were truly desperate for rifles. Going back to original Russian source, we find a production table of the Tula, Izhevsk, and Sestroretskij factories for the final months of 1914:

Year| month| Tula|| Izhevsk|| Sestroretsk|| Total|| Total| :--|:--|:--|:--|:--|:--|:--|:--|:--|:--|:--|:-- ||| New| Rep.| New| Rep.| New| Rep.| New| Rep.|| |1914| Aug| 3850| – |6446| 5695| –| –| 10296| 5695|15991| |Sept| 6653| 9900| 16036| 15436| –| –| 22689| 25336|48025| |Oct| 10255| 10100| 21031| 26536| 1130| –| 32416| 36636|69052| |Nov| 13120| 13120| 20078| 28189| 1990| –| 35188| 41309|76497| |Dec| 12000| 12870| 18530| 22041| 2780| –| 33310| 34911|68221| |Total|| 45878| 45990| 82121| 97897| 5900| –| 133899| 143887| 277786|

Note that rep. means repairs. In short, the Russian factories were more busy repairing damaged rifles than they were building new ones! Production at Sestroretsk didn't even get started until October.

I want you to keep in mind, in this same time period, the Russians would suffer heavy losses, amongst others at Tannenberg, where they would lose give or take 170,000 men, and presumably just as many rifles.

So, clearly, the Russians were in a bad spot. As a result, they would order foreign rifles and use captured rifles. There is an entire issue of supplying these rifles with the correct ammunition, but that's something I will have to skip in the interest of brevity.

To show the true desperation for rifles, we can list all of the rifles the Russians would use:

Rifle	Notes
Mosin 1891	Russian standard arm, 7.62×54mmR
Winchester 1895	American rifle using the Mosin cartridge and stripper clip
Arisaka Type 30	Japanese 6.5mm
Arisaka Type 38	Japanese 6.5mm
Mannlicher 1888	Austrian capture, presumably in 8×50mmR
Mannlicher 1895	Austrian capture, 8×50mmR
Berthier 1907	French 8×50mmR, supplied by the French
Gewehr 88	German capture, 7.92×57mm
Gewehr 98	German capture, 7.92×57mm
Berdan 1870	the aforementioned 4.2-line, Russian obsolete black powder
Gras 1874	French black powder, 11×59mmR
Gras-Kropatschek 1874/1885	French black powder, 11×59mmR
Vetterli-Vitali 1870/1887	Italian 10.4×47mmR

In short, 13 rifles in 8 different calibres. An armourer's worst nightmare. Although the book does not provide accurate numbers on all rifles (In fact, this would be nearly impossible for captured arms), 450,000 Gras rifles, 105,000 Gras-Kropatschek rifles, and 400,000 Vetterli-Vitali rifles would be delivered to the Russians.

On page 62, the book gives the following table of rifles promised (at an unknown date, perhaps for the entire war?), either by Russian factories or foreign allies:

Rifle	Number
M1891 Mosin	1 000 000
Vetterli	500 000
Gras and Gras-Kropatschek	560 000
Lebel	39 000
Mexican Arisaka	35 000
Japanese Arisaka	660 000
Austrian captured arms	300 000
Berdan 4.2-line	300 000
Total	3 594 000

Please note that Lebel might be a mistake and mean Berthier, as happens at other places in the book.

Now there is a different question which is to be answered, which is how are these rifles distributed? The nearly one million black-powder rifles noted above did not see front-line service, as a rule. In fact, these obsolete, fourty year-old rifles were issued out to rear-echelon troops and non-combat troops. Soldiers guarding ports, train stations in the middle of Siberia, that sort of thing. These troops would hand in their Mosins, which would be sent to the front, whilst their black-powder rifles were still okay enough weapons for guarding some base in Siberia. It's not as if there was a big issue of partisans there.

Finally, to more directly answer your question, it's my understanding that "one rifle for two men" is more of a movie myth. Yes, the Russian were truly desperate for rifles, their industrial capacity could not replace the lost rifles and they relied heavily on foreign production to fill the gaps. But even then, I think this myth relates more to World War II if anything.

I hope that answers your question.

Edit: Table formatting

Sources: ОРУЖЕЙНОЕ ДЕЛО НА ГРАНИ ДВУХ ЭПОХ: ОРУЖЕЙНОЕ ДЕЛО В ПЕРВУЮ ИМПЕРИАЛИСТИЧЕСКУЮ ВОЙНУ, Владимир Григорьевич Фёдоров, 1939

The Mosin-Nagant Rifle, Bill Harriman.