Sneak

Sneak is a Fallout, Fallout 2 and Fallout 3 skill.

Quiet movement, and the ability to remain unnoticed. If successful, you will be much harder to locate. In Fallout and Fallout 2 you cannot run and sneak at the same time unless you have the Silent Running perk.

Fallout, Fallout 2 and Fallout Tactics
Initial Level: Starting Sneak skill is equal to 25% + (1% x Agility). Average characters will have a 30% Sneak.

Fallout 3
Sneaking is one of the most important skills. The closer you can get to a foe without being seen, the higher your odds of hitting him, so this helps with every type of weapon; otherwise, you have to split points between different types of weapons or increase skill for one type at the expense of another.

Sneaking is also a good defensive tool. In a dark hallway, once your Sneak level gets high enough, a Super Mutant will run right by without seeing you.

Several items in the game will increase your Sneak skill (besides the obvious Stealth Boy). One is Recon Armor, which adds 5 to Sneak while worn, and Shady Hat, which adds another 5 and the Chinese Army: Special Ops Training Manual book which add 1 point per copy found (2 with Comprehension). One possible reward from the Oasis quest is Poplar's Hood which adds +10 (12 if you don't have 10 Agility) Sneak when worn.

Unlike its predecessors, in Fallout 3 a player can both sneak and run at the same time regardless of perks, however, without the Silent Running perk the player will suffer a detection penalty while running.

The stealth state is displayed while crouching: Note: As soon as the conditions are satisfied for any state it replaces the one above it on the HUD even though the player may still be in the HIDDEN state to several targets around them. Essentially, it reports the worst detection state towards the Player of all potential targets.
 * [HIDDEN] means undetected by everyone.
 * [DETECTED] means detected by a friendly target or multiple friendly targets.
 * [CAUTION] means enemies' attention is suspicious because of intermittent detection, such as a missed shot whizzing by their heads.
 * [DANGER] means detected by an unfriendly target or multiple unfriendly targets. If flashing, the enemy is aware of your position.  If steady, the enemy has lost your position but is still in an alert state and searches for you.

Successful sneaking is dependent on many factors:
 * Sneak skill: The Sneak skill applies whenever the player crouches. The higher the player's Sneak skill, the easier it is to remain undetected while attacking, stealing, or picking someone’s pocket.
 * Cloaking Fields: The Stealth Boy and Chinese Stealth Suit will wrap the user in a cloaking field that makes him more difficult to detect while sneaking. The stealth field effect is extremely powerful, and its value seems to not matter, so the Chinese Stealth Suit's stealth field of 5 works just as well as the Stealth Boy's 75.  The stealth suit only has a +15 sneak versus the stealth boy's +100, but its effects are not limited by time.
 * Enemy’s perception: Enemies with low perception are easier to sneak around than enemies with high perception. A target's perception will be impaired if they have a crippled head.
 * Line of sight: While out of sight an enemy can only detect the player through sound.
 * Light level: The player is more difficult to see in dark areas or at night if outdoors. The Pip-Boy light, while active, will make the player much more visible. Likewise, glowing weapons such as the Shishkebab and Jingwei's Shock Sword can give away the player's position.
 * Movement: The player is hardest to detect when motionless and easiest to detect when running. You are able to avoid the sound aspect of this by getting the perk Silent Running. Moving faster while within line of sight will still make you easier to spot, but you will no longer get any penalty for movement speed to your sound made. Pushing yourself into targets will immediately alert them to your location.
 * Equipped Weight: The total weight of all equipped items (weapons count only if they are in your hands) makes your footstep noise louder for NPCs. Silent Running removes this penalty entirely, allowing you full sneaking ability in any equipment. You will still hear your footsteps while sneaking with the perk, but NPCs never will.
 * Sound: Most guns make noise. Louder guns make you easier to detect. The Silenced 10mm Pistol, the Dart Gun, all melee weapons, and all unarmed weapons are considered entirely silent, even though you occasionally grunt when attacking with melee or unarmed and you hear some noise from the two others. Hitting but not killing an enemy with silent weapons still causes a CAUTION alert.  All other weapons will most likely be heard, depending on your distance from the target. Grenades (placed in an enemy's pocket or otherwise) and all other explosives make noise at their point of impact (although using them as a diversion isn't suggested because it still causes CAUTION status).  Missile Launchers and Fat Man units make noise at your location and then at the impact point as well.  Oddly enough, your Pip-Boy's radio has no effect on sneaking, nor does running into loud objects like shopping carts or tin cans.

Sneak-Attacking
Attacking while undetected by the target results in an automatic “sneak” critical if the attack hits. It is possible to miss a sneak attack which will result in probably detection by the target. For best results, maximize chance to hit as much as possible before attacking so the sneak critical is not wasted. It is possible to get a sneak critical while being detected by one target, friendly or unfriendly, on another target that has not detected the player if you act quickly before it has time to alert the other targets.

It is possible to kill an enemy without alerting those around them if the sneak critical is also a one-hit-kill even with loud weapons like the Assault Rifle. Additional attacks after the first, queued in V.A.T.S., will be treated as non-sneak attacks and will reveal the player's location to the target and possibly other enemies, presumably because the target then alerts their friends.

If the player can close to melee range of an enemy while remaining undetected by the target they can then be pickpocketed and a live mine or grenade can be added to their inventory. The explosive will detonate after a short timer automatically killing the target regardless of the player's explosive skill or the target's health or resistances. The explosion can damage or even kill the player if they do not move out of the area or take cover quickly. Its best to holster your weapon before attempting Pants Exploded, so you can crouch-run away as fast as possible, you only have 3 short seconds.

It should also be noted that when a player enters third-person perspective, they are able to peek around corners without being seen. This minor trick can be useful sometimes when sneaking to see what type of enemies are around corners or if there are any traps. Be careful when sneaking in dark areas or at night as you may accidentally step on a trap or landmine. This can be avoided with the Perk: Light Step.

Pickpocketing
While sneaking and [HIDDEN], activating an NPC will allow you to pickpocket them; in other words, steal items that they are personally "holding."

For each item you steal from an NPC's inventory, there is a chance (presumably based on your Sneak skill, Luck, and the NPC's Perception) that you will be detected. If detected, the NPC will automatically reclaim the item(s) you took and you will not be able to pickpocket that NPC again (leaving the area and returning 24 hours later should allow you to re-attempt).

You can not steal items an NPC currently has equipped. If you want to steal an item the NPC is wearing or using (armor or weapon), you can reverse-pickpocket a better item into their inventory and then leave and reenter the area. The NPC will equip the item with the highest stats and you will be able to steal the item he or she was using before.

Successfully stealing the ammunution from an NPC with a gun equipped will immediately render that NPC unable to fire their gun. The amount of ammo an NPC is carrying will not match the amount they could fire if not pickpocketed (which is actually unlimited); this discrepancy can be attributed to gameplay purposes. Because this renders NPCs able to use only unarmed attacks unless they pick up a nearby weapon in the gameworld, this tactic can be used to (strongly) influence the outcome of several NPC-on-NPC conflicts in the game without the player needing to personally participate in the battle. This allows you to remain non-hostile to NPCs (at least the ones left alive) on both sides of a conflict while still ensuring victory for one side or another.

Pickpocketing expensive or heavy items
Although not confirmed, but it seems that expensive items (e.g. minigun) are more difficult to pickpocket than cheap items (e.g. ammo). In order to increase the chance for obtaining an unique and expensive item from an NPC, reverse-pickpocket an item which has similar value into the NPC's inventory. Press E to Exit and wait around 10 seconds, then pickpocket the item you want and now you are likely to get it. (Tested with Eugene)

From my experience: The price of an item is not a factor (or, at least, it's not the primary factor); it is the weight of the item pickpocketed. The heavier the item, the more likely you will be caught (which makes complete sense, logically). Weightless items are not "freebies," however. There is still a risk of being caught with "--" weight items.

Stealing Items
Picking up NPC owned items in the game world while sneaking and [HIDDEN], will allow you to steal items undetected.

One easy way to steal items in shops (as in Rivet City) is to simply "grab" the item (gun, chem, food, etc.) by clicking the right thumb stick (Z key on the PC). You can then drag the item to a concealed area, go into sneak mode, and steal it without anyone noticing. This is a good way to acquire any goods you see on display or simply to collect items (like chems) to sell to another shop owner.