The Picard Maneuver involves warping from one location to another, within the enemy's visual range, then firing all ship weapons in an alpha strike. In general, the maneuver attempts to create a "double image" of the ship. If the defending ship is unprepared, it may waste its weapons fire on the image of the ship rather than true ship, resulting in the defending ship's destruction if the attacker's alpha strike can quickly overwhelm the defender's shields.
The Picard Maneuver was not widely used in the Dominion War, possibly because it is more advantageous to divert warp power to shields and approach heavily shielded. In TNG "Hero Worship" Geordi diverted fusion power to the shields, resulting in a doubling in shield strength.
Additionally, more accurate faster-than-light sensors could have rendered the Picard Maneuver obsolete. An obvious countermeasure to the Picard Maneuver is to fire at both the image and the true ship. The small number of total weapons on Federation ships does place limits on this possibility.
Picard himself rarely used the tactic in combat, possibly because he was aware of these pitfalls. The Picard Maneuver appears to rely on a tactical officer's inexperience in combat and slow human reflexes. A competent tactical officer could program his console to fire at the final position of a starship, rather than the image, and additionally could program his console to fire at an approaching enemy vessel without input. Such possible pre-programmed responses are evident in TNG "The Wounded" when the Enterprise-D raises its shields automatically to a sneak Cardassian attack, or The Final Frontier where the Enterprise-A detected an incoming Bird of Prey but was not programmed to automatically raise its shields.
The Picard Maneuver causes the target to see two images of the maneuvering ship. This happens because the maneuvering ship changes position faster than light. Light from its original position is still reaching the target when the ship arrives at its new, closer position; the target therefore sees the ship in two places at once.
The success of this tactic depends on the inability of the target to follow the faster-than-light movement of the maneuvering ship. This tracking limitation implies that at combat ranges, warships rely heavily on lightspeed sensors to track other vessels.
As far as we know, the Picard Maneuver has only been successfully used once. Captain Picard, then captain of the USS Stargazer, used it to counter-attack a Ferengi ship that ambushed the Stargazer, destroying the attacker in one salvo. Under the influence of a Ferengi mind-control device, Picard attempted to repeat the attack against the Enterprise, but knowing what to expect, the Enterprise crew were able predict where the Stargazer would drop out of warp by detecting the compression of trace hydrogen ahead of it, allowing them to immobilize the Stargazer with a tractor beam.. One would think that since they had experience with the maneuver, that they should know that the second, "new" image would be the correct one.