When it comes to infantry vs infantry battles, the sniper unit is king, and the Russian sniper regiment offers the cheapest way to get these units on the field. Although the sniper units of Japan, Russia, and Great Britian differ somewhat, their main advantage is the same: +250 damage versus infantry.
 
That means the sniper unit can kill almost any infantry unit in one shot, as fast as they can fire (every 10 seconds).
 
Even with the benefits of the sniper unit, the Russian sniper regiment usually depends on an advantage in numbers to be successful, aka spam. The supporting units are much weaker than those of SaS, or even Commandos (they at least have 1 mg unit per regiment). Russia also lacks the important special forces upgrade. But don't fret...
 
Russia has several advantages when it comes to spamming infantry.

Several of the Russian special ops are well suited for the infantry game, with the standout being Konev's three headed monster of Communist Zeal, Smoke Barage, and Military Gear-Up.

The Russian sniper was able to slow the German advance in the early parts of the war (1941-43), and was able to turn Stalingrad into what the Germans' called "Rattenkrieg", or "The War of the Rats". In the final months of the Battle of Stalingrad, Russia deployed so many snipers the only way for the Germans to stay alive, was to crawl through the rubble like "rats". A fictionalized story "The War of the Rats" was the basis of the film Enemy at the Gates.
 
The number of sniper kills attributed to some of the top snipers in WW2 have likely been exaggerated for propaganda purposes. In some cases no evidence that the person ever existed can be found, such as Mikhail Surkov (702 kills), and Erwin König (400+ kills)
 
One thing that cannot be disputed is the contribution of Russian women as snipers. Over 2000 women served on the eastern front as snipers, and were credited with 12,000+ kills, with many being considered as some of the top snipers of all time. One of the most famous was Lyudmila Pavlichenko (309 kills). After the tide of the war turned in 1943, the snipers that had worked so well in a defensive role, took heavy casualties in the fast-paced offensive demanded by Stalin. Germany adopted similar defensive tactics using snipers, and snipers proved to be much more effective at delaying an advance, than supporting one. In the harsh conditions, only 500 of these female snipers lived to see the end of the war.

The basic build will vary some depending on map size and starting money (if more than $500)

If you are planning an early game Sniper attack, or your base is located in the front, you might spend more on regiments and less on the HQ's (which bolster your economy). If you have plans on really getting your economy going, or your base is located in the back, you might spend more on HQ's and less on your armed forces. Of course this is an example of a multiplayer build (3v3, 4v4), if you attempt to eco this much in a 1v1 you would be quickly rolled...
 
Remember this is a spam regiment, don't even bother with snipers unless you plan on deploying at least 8 regiments, usually more.

When it comes to perfomance upgrades, Russia doesn't have much to choose from. The only upgrades they have that effect the units of this regiment are Marksmanship, Advanced Infantry Training, and Entrenchment.
 
For more info on infantry upgrades, see: Upgrading Your Infantry/Airborne

There are two different types of formations, formation on the regiment level (Assault, Aggressive, and Column), and formations on the division level, which are a formation of a group of regiments.

Groups of regiments can also be put in the Assault, Aggressive, and Column formation by activating group behavior, but this is not recommended for combat, only for reorganizing your division if it becomes too spread out. That means most of the time your division should have custom formations with group behavior set to off. This also allows you to set the formation for each regiment in your division without affecting the group formation.

You will want to use different group formations for different game situations, some basic examples are seen on the left and right. The determining factors are usually what type of enemy regiments you are facing, and how many special op bombs your opponents have. Hotkeys are essential for effectively managing your divisions, so once you have selected and organized a group, save it by holding down [Ctrl] and pressing any of the keyboard number keys; or simply right click an spot on the group control bar.
 
Of course there are many other factors that influence a successful infantry campaign, see conclusion for more tips and links.

Battling 1v1 in isolation, the sniper regiment doesn't dominate as well as it can when micro'd effectively. Left to their own devices, each regiment in a group will attack the closest target, which will often spread your sniper hits across multiple enemy regiments. This leaves the enemy regiments wounded but still alive, and gives them a window to retreat and heal.
 
The true power of snipers comes in groups, and focusing all their firepower on one enemy regiment. For instance, if you can take two groups of 5 snipers, and target one enemy regiment, 20 sniper hits is more than enough to kill any infantry regiment in the game; instantly. The trick becomes how to single-out an enemy regiment (which can be done in several ways). Perhaps the easiest method is to target an enemy regiment that has strayed too far away from the others.
 
Retreating to Attack - Using the retreat command and clicking on an enemy regiment will cause your troops to ignore any other target and pursue the enemy in column formation. This is a dangerous tactic which has many negative effects on your forces, most notably their morale and combat effectiveness, so use sparingly and carefully, if at all. This tactic deserves mention with snipers, since the +250 damage vs infantry is usually strong enough to counter any penalties you suffer; just keep your troops from routing or chasing enemies too far and getting pinched.

There is a point in the mid-to-late game where snipers are no longer an effective option for front line fighting forces. They can be used to capture cities on the outskirts, or they are often used in a defensive role, to protect your base from airborne attacks.
 
Order 3-4 regiments of snipers to guard your Corp HQ and let them entrench, and they can easily repel most airdrops. Eventually you will need to have fixed defenses for your base, so you can use all of your available 20 slots for armor; but snipers can delay that need until later in the game when money is more plentiful.