While the Law of Darkness primarily manifests itself as mere social conventions - a tendency to prefer the dark over the light, to presume guilt before innocence, and so forth - it does have two very important game mechanics. First, the power of darkness is such that it can overcome the Law of Reality, allowing full access to all game mechanics. Second, it produces an increase in the Magic axiom sufficient to grant life to creatures that require magic to exist. Both of these effects occur only under "true darkness", or the fall of night. Shadows, no matter how deep, are insufficient, though a solar eclipse might provide the neccessary blackness.
In game terms, characters receive a +1 to all actions taken towards a specific desire. These desires have to be more overall in nature - "aquire wealth", "rule the world" - rather than immediate - "defeat my current opponent", "escape this death trap" - and once chosen cannot be changed. (So even if it was a person's goal to defeat their immediate opponent, once defated, they wouldn't get a bonus until they met that opponent again.) The character can gain an additional +1 for further limiting the scope of their obsession - "gems", "rule the world of Botany" - and an additional +1 (for a toal of +3) for limiting it to a specific obsession - "the Hope Diamond", "creating the first true Black Orchid". (Again, once determined, the Obsession cannot be changed, and more than one Gotham-ite has achived their life's dream, only to be driven to extremes by their happiness and the knowledge that they can never again reach their goals...) Also, whenever the object of their obsession is used against them - as the means of a Taunt or the goal of a Haggle - the character not only does not receive the bonus, but actually suffers their Obsession as a penalty. (It is quite possible that both sides of a transaction will be so blinded as to not care what the other wants!)
Example: John Doe has a need for speed. Any skill checks to go faster, such as pushing running or driving a land Vehicle, are made at +1, as are any Scholar checks about information on the fastest animal, or land speed records and any Science checks involving velocity. If John Obsessed only about cars, he would get a +2 on all driving checks, knowledge about specific makes or models, and attempts to repair or improve cars, but no bonus at all on airplanes, cheetahs, or simple velocity. Should John instead narrow his Obsession to restoring his antique Finger-Kane '38 roadster, he would get a +3 on all repair rolls, Streetwise checks to find rare parts (but be at -3 when Haggling on the price!), and even Artist(Painting), since he would never let another person close enough to paint it instead. But should the roadster ever be fully restored, his Obsessive energies will have to find a new outlet. If he is very lucky, he might find another '38 F-K roadster to refurbish (and another, and another...), but more likely he will find himself destroying the car himself so that he may continue to repair it, or end both of their existances with a suicidal plunge off an oceanside roadway. Things rarely work out for the best in Gotham.
Note: The GM should feel free to award an additonal possibility to those characters that roleplay their obsessions to the fullest, as if it were a Subplot. In addition, many subplots that can deal with Obsession, from Personal Stake to Romance to Nemesis and so on, are worth two (2) possibilities per act to those operating under the Law of Obsession.
In game terms, a number of the mechanics that simulate "luck" or "action" are not available in Gotham. Rerolls are not allowed, for Skilled or Prated. Rolls can still be modified by the expedniture of possibilities, but the cost is doubled. (It now costs two possibilites to buy a reroll. In this case, more than one personal possibility may be spent to modify a roll, but still only one modification per roll can be bought through personal possibilities.) The cost to buy off damage is similarly doubled. (As is the limit, and again, only three "packets" per attack may be bought off through personal possibilities.) Also, Prateds take damage on the Ord Combat Results table, and any Wounds taken will suffer penalties. (If the GM is already using Wound Penalties, the effects are doubled. In the case of a Wound Subplot in Gotham, the effects would merely be tripled, not quadrupled.) All of these effects, however, are can be negated by the Law of Darkness at night, which is when most important things are done in Gotham.
Look in on some of the Personalities of Gotham.