Liam O’Flaherty establishes the tense, ominous, violent mood of the story in the first paragraph by describing the atmosphere of Dublin under siege during the Irish Civil War. O'Flaherty depicts the twilight sky, which corresponds to the dark, dangerous conditions in the "beleaguered Four Courts" as the Republicans and Free Staters engage in battle. The dim atmosphere and continuous sound of artillery fire throughout the city also adds to the suspenseful, threatening atmosphere of Dublin.

As the night sky darkens and the waters of the Liffey become black, enemy soldiers shoot at one another while night gradually approaches. O'Flaherty's ominous mood is fitting for a short story focusing on the Irish Civil War. Throughout the short story, O'Flaherty explores the effects of the civil war on Irish citizens, soldiers, and family members. In the first paragraph, O'Flaherty establishes a suspenseful, ominous mood, which correlates to the dark, gloomy atmosphere of the beleaguered city during the Irish Civil War.

Let's start with the mood and atmosphere of the story as a whole.  I would say that this story's mood is tense, dark, and violent.  In a nutshell, the story is about a sniper that coldly shoots and kills three people.  One of them happens to be his brother.  

The opening paragraph helps to establish that mood by setting the story in the evening.  Day is fading into night, so there is an actual darkness that accompanies the emotional darkness of the story.  

The long June twilight faded into night. Dublin lay enveloped in darkness but for the dim light of the moon that shone through fleecy clouds, casting a pale light as of approaching dawn over the streets and the dark waters of the Liffey.

Notice all of the words that focus reader attention on darkness and dark times.  "Twilight," "faded," "night," "darkness," "dim," and "pale" all highlight an ominous and oppressive feeling.  The rest of the opening paragraph points readers toward the violence that is happening around the setting.  A civil war is going on and guns can be constantly heard.  Based on the opening paragraph, readers know that this story is going to be a dark and violent story. 

In Liam O'Flaherty's short story "The Sniper," describe the atmosphere and explain how this is created.

The atmosphere in Liam O'Flaherty's short story "The Sniper" is created through the story's diction (word choice) and additional imagery in the form of literary devices.

Words and phrases that are used in the story's introduction include darkness, dim light, dark waters, beleaguered, guns roar, machine guns, and rifles.

Dublin lay enveloped in darkness, but for the dim light of the moon...

And...

Around the beleaguered Four Courts the heavy guns roared.

These carefully selected words and phrases—which are representative just of the first paragraph—produce mental images for the reader of the story's mood, just as the author intends. Darkness is a strong motif in the story. 

The solemn mood generated in the first paragraph is continually woven throughout the fabric of the story. Other words include cold gleam (often associated with a gun), fanatic, death, and again, darkness. The motif of darkness is perpetuated as the story develops. For example, when the Republican sniper tries to smoke a cigarette, the light from his match draws the attention of the enemy sniper who shoots at the light, and the brief illumination is distinguished. This foreshadows a sense that light will not soon return to the sniper's life nor to Dublin (nor the country of Ireland).

Using personification, an armored car is described as "panting" and is later called "the grey monster."

By the time the Republican sniper stops to see if he knows the identity of the dead enemy sniper, the darkness of the story's message has prepared the reader for the tragedy exposed in the story's last sentence.

Then the sniper turned over the dead body and looked into his brother's face.

How could one describe the atmosphere prevalent in Liam O'Flaherty's short story "The Sniper?"

When Liam O'Flaherty wrote his short story "The Sniper," it was within the context of the brutal conflict being waged in Ireland between Catholics and Protestants, the latter seeking to retain Northern Ireland's status as part of Great Britain, the former determined to rid Ireland of English Protestantism and to break Britain's hold on its smaller, weaker neighbor.  "The Sniper" takes place in Dublin, the capital of Ireland.  It is summer.  O'Flaherty describes the scene as "twilight," when the city "lay enveloped in darkness, but for the dim light of the moon that shone through fleecy clouds . . ."  The action takes place on Dublin's rooftops, where snipers from both sides in the conflict lie in wait for targets to appear.  Because of the darkness and the endless obstructions characteristic of urban cityscapes, visibility is extremely limited, and the unconventional nature of the conflict -- urban guerrillas attired in regular civilian clothes rather than easily distinguishable military uniforms -- the potential for accidents ("friendly fire" being the euphamism commonly employed) is always high.  Making that potential greater still is the fanaticism and determination to kill the enemy that permeates many fighters in a war.  O'Flaherty describes his "protagonist" as young and determined:

"His face was the face of a student, thin and ascetic, but his eyes had the cold gleam of the fanatic.  They were deep and thoughtful, the eyes of a man who is used to looking at death."

Wars are fought by the young, and "the sniper" is presumed to be just another irregular soldier in a civil conflict of indeterminate duration.  But the tension is palpable, as O'Flaherty sets the stage by noting that "heavy guns roared.  Here an there through the city, machine guns and rifles broke the silence of the night."  The sniper is shot in the arm, adding to the tension and the difficulty of his task.  He can no longer hold his rifle properly to aim and fire, so uses his revolver.  Under the circumstances, that his victim in O'Flaherty's story is revealed as someone known to the sniper, while ironic, is perfectly consistent with the atmosphere in which "The Sniper" takes place.