I've got a GREAT book written about the British side of it, Martin Pegler's Sniping in the Great War which goes into how at the beginning of the conflict, the lack of specialized marksmen weapons was so great that officers were having family members ship them their custom hunting rifles/optics, and relief charities held drives and purchased accurized civilian weapons, and captured German Gew88's fitted with scopes were highly prized as well.

Initially, snipers were either volunteers or just whomever they issued the nice rifles to. There was very little formal training, very little criteria to meet other than being willing to take on the job. Snipers worked in two ways:

• The first was to simply set up a clever blind within the trenches, armored with a glacis plate and extra sandbags, keeping their rifle trained on one specific spot on the enemy trench line where people were known to congregate, or an established firing position. Any time a flicker of motion or light happened at that spot, they'd send a round after it, hopefully killing a German. As time went on, the best shots would go on to becoming instructors, and by 1916 actual "sniper schools" were being held far behind the lines.

• As sniper-craft developed, things got more interesting. Herbert McBride writes in With The Emma Gees (a history of his time in the Machine Gun Corps) that in late 1915 he drew a Ross rifle equipped with a Warner and Swazey optic from the Quartermaster, and basically taught himself how to be a sniper. The British would pound an enemy line with massed machine gun fire and artillery at night while sharpshooters and relief machine gun crews moved from the first/second line trenches out into No Man's Land, setting up shop in abandoned houses, camouflaged redoubts, and deep shell craters.

McBride was an especially good shot, and benefited from working in concert with a machine gun crew. If 1-2 Germans revealed themselves, he'd open up with the rifle. More than that, and they'd lay down a pattern with the Vickers gun, it already being sighted in and all ranges known exactly through careful preparation and calculation. There's a whole chapter about "Sniper's Barn", a very well-concealed hide in the ruins of a barn, where he and his men would continually go to score kills.

Another interesting bit of trivia is that the Mk. VII .303 British general service cartridge didn't extract from belt-fed machine guns very well, so the British Army introduced the Mk. VIII, which had a greater maximum range and better feeding characteristics due to a larger powder charge. The Mk. VIII was forbidden to be used with rifles, because the increased pressures caused significant erosion of the rifle bore. However, the extra velocity/range was prized among both snipers and regular troops, who laid in a supply against orders whenever they could.

If I could ask a follow up: Periscope rifles were developed as a technological advance to address the high casualty rates seen in the trenches among snipers. How effective were they? The general consensus seems to be "not very" but I don't have many good sources.

An excellent take on this would be the memoir of Will Bird, published as "Ghosts Have Warm Hands." In it he relates how shortly after he arrived on the Western Front, in early 1917 he was assigned as a sniper with no particular special training beforehand, but going out under the tutelage of an experienced sniper. He records four kills during his first (and only) time actively sniping, giving up an opportunity for a fifth saying "A queer sensation had spread over me like nausea", later telling his Sergeant he had "all I wanted of sniping."(Bird 22) Shortly after he was evacuated from the lines suffering from mumps and thus missing the Battle of Vimy Ridge, but later returning to his unit for service at the front for the remainder of the war in a rifle section. Although Bird makes no mention of it, it is entirely possible that the rifle he used was the Canadian made and very controversial Ross Rifle. Found to be prone to catastrophic failures under rapid fire conditions, the Ross had been phased out for the more robust Short Magazine Lee-Enfield by this time. However, the Ross' reputation as a fine sporting and target rifle ensured that it was still a weapon of choice for snipers throughout the war.

For an American/late war take on this, I'd recommend reading "Scarlet Fields," which is a republished memoir by John Lewis Barkley. Barkley was part of what was called an Intelligence Unit, which covered jobs like scouting, sniping, capturing enemy soldiers and officers, and spotting for artillery. As I recall, he was just picked out of basic training for the job, probably for displaying some potential for such duty.

As a side note, Barkley is also a little known Medal of Honor recipient- apparently he almost single-handedly stopped a German counter attack during the Meuse Argonne offensive by capturing a German machine gun, setting it up in a disabled tank, and killing something like 500 enemy soldiers. Hard to say what's real and what's embellished, but it's a great read either way.