This is a good introductional video to basic sniping techniques by Lon Horiuchi who is a former U.S. FBI sniper who gained notoriety after his role in the Ruby Ridge shootings and the Waco Siege. The video goes cover position, breath control, trigger pull and various other things. I think the music is pretty horrendous...

A sniper is an infantry soldier specializing in shooting with a rifle from a position of concealment, and usually from longer ranges than is a regular infantryman, often using a specially designed or adapted sniper rifle.

The word sniper stems from at least as early as 1824 in the “sharpshooter” sense. The verb to snipe — British soldier argot, circa 1770s British India- means: “to shoot from a hidden place”, and possibly alludes to snipe shooting, for the snipe is a game bird known as extremely difficult to find, approach, or shoot. It has been contended that because hunters skilled at hunting this bird were dubbed “snipers”, hence being a sniper requires skill in marksmanship, camouflage, and field craft. If this is the etymology of "sniper" it is curious, because fast-flying snipe are typically shot at distances of < 40 yards using pellet-scattering shotguns, while a sniper fires a single projectile at a normally static target at long distance.
More recently, the word “sniper” has been rather loosely used, especially by news media in referring to police precision riflemen; an assassination rifleman; any shooting from all but the shortest range in battle; and any civilian criminal armed with a rifle. During the Bosnian War and the Siege of Beirut, “sniper” referred to soldiers terrorising and killing civilians by shooting from high windows and roofs; during the Siege of Sarajevo, its main street was known as “Sniper Alley”.

This loose usage expanded the word's general definition, and attached mixed connotations to it: official spokesmen tend to use other, compound words, especially for police department snipers - “counter-sniper”, “precision marksman”, “tactical marksman”, “sharpshooter”, or “precision shooter.” Some of these alternative words are now commonly used, but most are euphemisms.