In the original Star Trek universe, "deflector" shields in fact do no such thing. They do not deflect, they shunt the energy that is poured into them, be that energy kinetic, beam-weapon, or explosive, directly into their generators. This results in fragile, easily-penetrated shielding that usually offers a minimum of protection for a maximum of output energy.
The shields of Heisenberg's universe, however, use varying technologies depending on their purpose.
Navigational deflectors adjust the trajectory of micrometeoroids, space dust, and so forth by applying a subspace-based antigravity field at a modest distance from the hull. For example, Heisenberg's nominal navigation shields function at ten meters from the surface, permitting EVA work on the skin of the vessel without interruption. Further, the shields will keep objects inside them in, so that if a work crew loses a wrench it does not spin off into the infinite black, but can be handily transported back onto the ship later. These shields are relatively simple, and are emitted from one large transmitter integrated with the ship's primary forward sensor array in the engineering hull, with other sensor arrays featuring much smaller emitters designed to boost the field's signal strength.
Subspace-augmented repulsor fields or "forcefields" are the logical end result of investigation into technologies to help people who shouldn't be moving around stay put. They, like the navigational deflectors and the system of gravity used on all starships as of 2391, are an extension of gravitics research in the middle of the 22nd century; once you have a machine which exudes a gravitational field and holds people down, it's a simple enough step to turn that inside-out and produce a repulsive force.
Forcefields are constructed as if they were a sheet of antigravity, held in check by a subspace envelope. Anybody attempting to penetrate the forcefield will experience a great deal of resistance as if pushing against a wall; it also returns momentum, so someone throwing themselves against it results in being thrown backwards again.
Forcefields find one use in the civilian world in the form of trampolines - forcefields are placed across the rubber surface of a trampoline to prevent the user injuring themselves by landing on the springs or passing a leg or other extremity through the holes between them.
Defensive shielding, more often referred to by the colloquialism "shields", is a much-stronger form of forcefield. Formed of several layers including projected gravitational and subspace fields, a starship's defensive shielding provides protection from most forms of attack. Before shields are raised, all EVA activity must cease and any transporter operations ongoing must be concluded as the high-resolution sensors and warp pathway needed for transporter operation cannot transpenetrate even the lightest shield under normal circumstances.
Defensive shielding attempts to disperse incoming energy through dilation, absorbing and distributing the energy across a much larger surface area than would otherwise be possible. An incoming torpedo, for example, will be caught by the multilayered shielding and detonate within, spreading its shrapnel and radiation across all layers of the shield. This effort comes at a price, though - The emitters used to power the shielding are prone to brownout or destruction through excessive heating after enough abuse.
The primary difficulty inherent to shields involves their deployment and retraction. Charging and activating a defensive shield over an entire spacecraft involves several seconds, depending on factors such as the quantity of power available, the size of the area to be covered, the level of shielding required, and the number of functional generators. Some examples: to bring the Heisenberg's shielding to maximum requires eight seconds at full combat readiness, due to the availability of a second warp core for power. The USS Defiant requires less than one second, due to the large quantity of hull space allocated to shield emission, and the USS Galaxy takes a full thirty seconds to erect full shielding. Safely retracting shields involves giving the emitters the time necessary to sink heat into the ship's brannon-based cooling systems. Lowering shields takes approximately half the time required to erect them.
Defensive shielding is constructed in such a fashion as to permit subspace radio broadcasts, such as Identify Friend-or-Foe (IFF) beacons, standard communications, and so forth. The shields' surface can be "opened" selectively around weapons ports to permit firing of particle beams, as well. Torpedoes carry a tiny defensive shield designed such that it allows passage through the shielding of the ship that fired it and immediately burns out; in this manner it is possible to fire torpedoes through your own shields.
In a pinch the warp-relay frequency of transporters can be synchronized with the shields, to permit emergency transportation through the normally-impenetrable subspace barrier. However, this is extremely risky - anything that alters the operating frequency of the shields, including being fired upon, runs the risk of damaging the coherence of the warp field and flinging the flicked target into your own shields at velocities exceeding c. The result is seldom pretty.
Cloaking technology is an extension and alteration of defensive shielding. A cloaking field is relatively swift-erecting and does not block incoming particle beams or missiles any more so than standard navigational deflectors. However, light coming in on one side comes clean out the other side, with barely any distortion. When a cloaking field is engaged, the ship it is attached to deactivates all subspace radio transmissions and cuts power to its weapons systems; adding secondary layers of cloak shielding to disguise these emissions result in a swift 'baking' of everything inside the field as the high-energy plasma from the impulse drive heats the spacecraft's hull.
Cloaking fields need to be precisely calibrated in order to account for incident interstellar hydrogen; if the cloak is imbalanced then the vessel emanates small but measurable quantities of low-energy electrons and positrons. This property also makes it impossible for a vessel to cloak effectively in a nebula. Cloaked spacecraft under motion in excess of warp 5 "shimmer" as micrometeorite impacts dampen the cloak's effectiveness.
The technology required to establish and control a cloaking field is complex - a special set of computers and various other modifications to the shielding systems. Typically, these systems are condensed into a single, large module called a "cloaking device" that can be interfaced easily with the shield grid's projector systems at a central point. It is standard for Federation spacecraft to carry the replicator patterns necessary to construct one, such as the model FCE-5 which the USS Heisenberg is equipped to install. These patterns can be unlocked with the authorization codes from the Captain, Chief Engineer, and Security Chief.