The equipment and techniques of the artillery were those of WWI, but the unusual circumstances led to its employment being quite different.
Guns were spread down to regiments, and even battalions, rather than clumped. It was rare to see any more than a four gun battery operating together, and usually it was platoons – or even single guns. This allowed them to actively support the dispersed and mobile nature of the civil war battlefield.
Most artillery actions were in support of the troops, with counter-battery fire generally only happening when the opposition artillery was similarly positioned. This allowed guns to operate much of the time over open sights, which gave more immediate responses and was particularly useful when the crews were unskilled but brave. As the Red Artillery improved during the course of the war, the ability to fire indirectly grew, but even then they would almost always be near the front lines and directed by an observer only a short way forward. Long range indirect fire was largely the province of the large guns mounted on trains, who had specialist knowledge and could easily transport the technical means required.
Much of the effect of artillery in the civil war was moral. Troops were unable to sustain long periods under fire, even at the slow rates that ammunition supply for the period allowed. Thus we read of units falling back from positions after a few hours of a "harassing fire" that in WWI would takes weeks to have an effect.
Artillery density remained low throughout. The Western Front at the peak of the Polish War in August 1920 had 600 guns to cover 200 km of front, and it was half that on the Eastern Front in 1919.
Only prepared positions would field high densities, and then generally in the defence of a fortified area. The highest concentration I have seen for the Soviets is around 25 guns per km defending the crucial point of the Tsartisyn in 1918 (a tenth of what the British fielded at Ypres with higher calibres). In these situations all the technology of WWI trench warfare would be used, with centralised control via telephone and specified fire zones.
The first problem facing the new Soviet artillery was the extreme shortage of trained artillerymen, and most especially commanders. Sailors were pressed into this role because of their experience, though more commonly into the artillery on the armoured trains (which were often naval guns).
The employment of the military specialists helped ease this problem significantly. Eventually red commanders came through the new training programs. It helped that in the RCW the technical demands on the artillery were not high – without the creeping barrages and counter-battery threats of WWI – and so did not require long courses.
A much bigger problem was the ammunition. The Soviets had a massive advantage that they controlled the factories making both the guns and the shells for the standard artillery pieces of the war. But there are sufficient comments about Red artillery being on target, only to not explode, that suggest the quality of the ammunition, and especially the fuses, was often very poor.
Also like all armies of the war, even when there was sufficient ammunition, getting it to the front lines in good time was a problem. Units were habitually short of ammunition, especially when the front lines moved quickly.
The initial formations of the Red artillery were individual batteries, with random numbers of guns, attached to units or columns. This was ineffective, as supplying them was difficult and they could not be deployed flexibly.
Slowly the Red Army attempted to organise them into some sort of order, at least with the light guns. Artillery battalions (divizions) were formed, each of three 4-gun batteries. Strenuous efforts were made to stop units regarding batteries as "theirs". This meant that while still able to attach batteries to lower units, a divisional commander could at least ensure that his guns were able to be sent where most needed.
Heavy artillery was theoretically in divizions of three 2-gun batteries, but this was only rarely achieved.
Because the guns in action tended to be dispersed to regimental and battalion commanders, the division artillery commander's role was largely organisational and material.
Being so close to the front lines left the artillery very vulnerable to opposition infantry getting into rifle range, or cavalry getting behind a flank, many batteries had integral MGs to help protect them from this. Horse artillery had tachankas for the same reasons. (Most orbats that go that low include MGs with the artillery and they are mentioned in the memoirs of artillerymen, but I don't know if it was more or less universal.)
Red artillery should normally be light guns and dispersed to regiment level or below, unless a prepared attack on a fortified position, river crossing etc is being gamed.
The lack of ammunition precluded long bombardments in most battles. Even a positional defence might only get a couple of hours, and the "softening up" in open field would be far shorter than that. Thus some form of ammunition supply rule should be in force to prevent artillery from firing away all game at everyone in range. Targets were not selected unless there was a practical tactical reason, in order to preserve ammunition.
Guns should fire over open sights, or with a slightly advanced observer, unless in well-prepared positions.
Placing a section of MGs with any battery, tachankas for the horse artillery, would appear to be common.
The effect of artillery on the enemy would seem to be comparable to early WWI. The far lower quality of the actual artillery being largely compensated for by the lack of ability of the troops of the civil war to bear that fire.
Red artillery fire was definitely inferior to AFSR and NW Army artillery. The Whites had a much higher number of fully trained and experienced officers and had material and training supplied by the British. The poor quality of Soviet ammunition also lowered their effectiveness. However, their morale would appear to be similar.
My estimate is that other White and Polish artillery were very similar to Red. The Poles appear to have been keener on indirect fire using observers though.
Other nationalist artillery was often very poor, especially the UNR. The one exception was the UGA, whose artillery was their best arm due to the large number having served in the Austrian artillery.
Red artillery wore the same mix of uniforms as the rest of the army. The old crossed-cannons of the Tsarist army might be worn on the hat.
However many of the commanders were ex-Tsarist voenspets, so might well be wearing basically their old uniform – minus shoulder-boards and cockade, of course. That could also mean blue or black trousers. Red commanders preferred to wear red trousers, if they could find them.
This is an interesting look at the Red Artillery in the Civil War. Sadly it does not cite the sources of its statistics.
I don't have a lot if interest in the actual weapons themselves, but in case you do I have linked to the various Wikipedia pages for them.
A modern recreation of the Putilov 3 inch gun
The workhorse of the artillery was the 3 inch (76-mm gun) Putilov model 1902.
This was a sturdy and relatively simple gun. Because the factories that produced it and its ammunition were in the Soviet heartland, it quickly became the gun of choice and dominated the Red Army.
The horse artillery used the 3 inch (76-mm gun) mountain gun model 1909.
While it had its faults, this gun was light and mobile and ideally suited to the needs of cavalry in the civil war. Large numbers were left over from WWI.
A few 4.2 inch (107-mm gun) Schneider model 1910 were left over from WWI, and a handful more were manufactured during the war by the Putilov and Obukhov plants.
The most common howitzer was the Russian version of the Schneider 4.8 inch (122 mm) howitzer Model 1909, although there was also a very similar Russian version of the related Krupp 4.8".
I believe that the most common larger gun was the Schneider 6 inch (152 mm) howitzer Model 1910.
There were some British and French field guns captured from the Whites pressed into service by the Reds. The lack of parts, their increased difficulty to use and shortage of ammunition never made them common.
A few other very large guns left over from WWI were placed into units in Petrograd, potentially for defence of the city. Some were later transported to Kakhovka, but lack of parts and difficulty in transporting them made them useless in practice.