ST Shields
Most starships in Star Trek use defensive shield technology to protect against enemy attacks. As the shields take damage, they become weakened and effects from enemy attacks bleed through with greater frequency.
Nature
Shields are usually depicted as a bubble surrounding a starship that is visible only when actively resisting an attack. During the Dominion War, shields seemed to conform to the hulls of the starships projecting them.
Most transporters cannot beam through combat-grade defensive shields.
Capability
The shields of starships are typically capable of withstanding several attacks from opposing ships of similar size and technology. Blocking incoming fire steadily depletes the protective capacity of a shield, the reduction usually being described as a percentage of its full capacity.
Shields often perform poorly against new threats. For instance, Federation shields performed poorly against the phased poleron beam weapons used by Dominion warships during early battles, but Federation engineers were able to modify their shield systems to provide protection in later encounters.
The size, shape, and operating frequency of a shield is typically adjustable. All of these factors can affect a shield's performance against various types of attack.
Star Trek shields handle radiant energy far more effectively than collisions with massive objects.
Even with fully operational shields, it is not unusual for ships to sustain some internal damage when hit by weapons fire.
Vulnerabilities
Shields operate at a specific frequency. This allows friendly weapons fire originating from the shielding ship to pass through. If an attacker can detect the ship's frequency, such as in Generations, shields are ineffective. Many species such as the Borg, Vidiians or Voth, either explicitly or implicitly bypass shields in this manner.
The effectiveness of countermeasures depends greatly on the competence of the tactical officer and bridge crew. In Equinox Tuvok altered the shield frequences without prompting from Janeway. However, in Generations, Riker did not order shield frequency rotation despite previous experience with the Borg.
In The Wounded, O'Brien exploited a vulnerability in USS Phoenix's shields to transport himself through its shields.
The Emergency Medical Hologram was able to monitor the shield frequency of USS Voyager from sickbay in Equinox.
Tactics
In Hero Worship, Geordi diverted fusion power to the shields and doubled the Enterprise-D's shield strength. Diverting warp power to the shields would provide at least this much, if not far more powerful shields.
In Kirk's era, it was standard practise to raise shields on approach of an unidentified vessel. "Defense fields" automatically engaged, possibly to prevent indiscriminate transporter use. However, main shielding had to be activated by the tactical officer manually. It is unknown to what degree defense fields exist in Picard's era.
Shields can be extended from one vessel to another, as in Equinox.
Once an enemy's main shields are down, boarding parties generally transport themselves onto enemy starships. Why the boarders do not simply transport their enemies away is unknown. It is likely defense fields are independent units, separate from the main shields so when the main shields fail defense fields still provide a minimal defense against transporter assault. It is entirely possible that enemies in Star Trek are too stupid to think of beaming away crew rather than the dangerous task of boarding. However, this is unlikely, as a commander intelligent enough to think of beaming aboard a ship would think of beaming foes away. Another possibility is power use. In The Search for Spock and other examples transporter power was a serious issue.
Surprisingly, targeting the shield generator almost never occurs. This is possibly because penetrating the shield itself to attack the shield generator specifically renders the point moot.