
Radyn |

If I’m bitten and fail the save against “curse of the werewolf” during nighttime under a full moon, do I transform right away? Or is there an incubation period until the next full moon?
Also, I’m surmising that a full moon is 3 nights, is this correct?
Thanks anyone!

Pizza Lord |
A creature that catches lycanthropy becomes an afflicted lycanthrope, but shows no symptoms (and does not gain any of the template’s adjustments or abilities) until the night of the next full moon, when the victim involuntarily assumes animal form and forgets his or her own identity. The character remains in animal form until the next dawn and remembers nothing about the entire episode (or subsequent episodes) unless he makes a DC 20 Will save, in which case he becomes aware of his condition.
Different worlds are different, but in ours, typically a full moon lasts around 3 days (where we would classify it as a 'full moon' for astrological purposes). So if you are bitten and afflicted on the first night of a full moon period, you will turn into a werewolf on the second night. If it was the third and final night, you would show no symptoms for one lunar cycle (normally a month) until the first full moon night of that lunar phase.
It's worth noting that usually you only catch the Curse of Lycanthropy from natural lycanthropes and those can change form pretty much whenever they want (there are curses that can do it), so if you're bitten at lunch time during the day of a full moon you might only have an couple hours before it happens. If bitten right before moonrise or night falls (if the moon is already up), then it might be only a moment or two. Obviously if bitten and afflicted during a waxing half-moon (moon is becoming full), you might have half a month.

Derklord |

If on Saturday you say "I'll visit my family next weekend", it doesn't mean today, but rather in seven days. "Next full moon" would/should follow the same principle.
PCs shouldn't really trigger lycanthropy (as in the involuntary transformation), it's more of a quest to remove it than something that just happens. The reason we play is to control a character, and infliced lycanthropy takes that away from you. The transformation triggering immediately would go against the spirit of the game, in my opinion.
Also, I’m surmising that a full moon is 3 nights, is this correct?
Not explicitly written, but from what I can see in Blood of the Moon and Inner See World Guide, I think it's just one night.

Pizza Lord |
Also, I’m surmising that a full moon is 3 nights, is this correct?
While different worlds are different, and some worlds or planets have more than one moon (which will potentially have their own lunar cycles of new to full), thus requiring a GM to make their own calls on any effects that might occur, in the case of our world and Golarion, those moons follow the same phases. In those specific instances, a full moon is a three day period. So afflicted lycanthrope attacks will generally occur over a night or two, and then fade away for a month.
This might be different in some specific, geographic location on a planet where the moon overhead doesn't reach full due to the location of the planet and its angle of view or something, or where a moon might be full for more or less days depending on how it orbits its host (is its orbit flat or on an angled tilt?) but I can't go into those specifics.
It might not be explicitly mentioned in many places, but in regards to moon phases, I believe it's been noted and extrapolated from multiple different rules or rulings and notes.
Golarion Moon Phases

Mysterious Stranger |

I have to agree with Decklord on this. The next means the one after the current full moon. That is the way it works in any horror movie that involves werewolves. It also gives the character a chance to remove the curse.
A remove disease or heal spell cast by a cleric of 12th level or higher cures the affliction, provided the character receives the spell within 3 days of the infecting lycanthrope's attack. Alternatively, consuming a dose of wolfsbane (Pathfinder RPG Core Rulebook 560) gives an afflicted lycanthrope a new Fortitude save to recover from lycanthropy.
If the curse took effect right away the above section makes no sense.