Fallout, Fallout 2 and Fallout Tactics
This trait reduces the Action Point cost of all throwing and firearm attacks by 1, but does not allow making Aimed Shots. Despite the description, in Fallout, it actually reduces the cost of all weapons, not just throwing and firearms. This was changed in the later games.
When combined with 10 Agility, "Bonus rate of Fire", "Sniper" and a turbo plasma rifle, it gives the player character 5 single-shot attacks per turn on average. Adding two ranks of "Action boy" into the mix allows for 3 consecutive bursts from a heavy weapon.
In the demo, the Vault Boy image for this trait is used by the Small Guns skill. Its filename also says "AMDIDEXT" (apparently for "ambidextrous"), as though it could have been an opposite of the One Hander trait.
Fallout: New Vegas
This trait reduces accuracy with energy weapons and guns by 20% while increasing the fire rate by 20%. This reduction in accuracy reduces the chance to hit when firing in V.A.T.S. and increases the amount of sway when taking zoomed shots out of V.A.T.S. This trait does not increase the firing rate of automatic weapons.
Fast Shot is arguably better for sniper weapons. For example, the anti-materiel rifle has a spread of 0.015 and a fire rate of 0.4. With Fast Shot, this would increase to 0.018, and the fire rate increases to 0.48, a negligible difference either way that would probably not see influential use.
Fast Shot multiplies attack speed by 1.2 and accuracy by 0.8, while Trigger Discipline multiplies attack speed by 0.8 and accuracy by 1.2. So you end up with a 4% (= 100% - (100% * 0.8 * 1.2)) decrease of both accuracy and attack speed if both traits are taken.