In "Star Trek via Ghostbusters: Character Basics," I briefly described how Luck and Goals operate. Here is the lengthier version.
Luck
Instead of Brownie Points, characters have Luck (although some crewmembers prefer to think of it as "Achievement Points"). Luck can be saved, used as bonus dice, expended to reduce injury, or spent to improve Traits. Player characters start with 20 points of Luck.
Advancement
There are three methods of character advancement. Two of them, Mission Goals and Personal Goals, involve the awarding of Luck. The third, career advancement, does not.
Mission Goals
Mission Goals are the objectives issued by Star Fleet Command that starship crews are obligated to fulfill. When a crew accomplishes its mission, each crewmember is awarded Luck commensurate with the mission's level of success or failure.
For a failed mission, each crewmember is awarded half the Luck spent.
For a barely successful mission (such as success achieved at a high cost), each crewmember is awarded all the Luck spent plus one or two.
For a resoundingly successful mission, each crewmember is awarded half again the Luck spent.
In general, Mission Goals are accomplished by the efforts of the entire crew.
Personal Goals
Characters may also earn Luck through the pursuit of Personal Goals. In the United Federation of Planetsand Star Fleet in particularmany of these are influenced by a desire to promote the common good. At the Trek Master's discretion, player characters may be permitted to change their Personal Goal before each adventure. Players may select from the following list of Personal Goals or suggest their own.
Peace: Characters whose Goal is Peace gain 1D6 Luck points when their actions contribute to establishing peace between two hostile parties.
Order: Characters whose Goal is Order gain 1D6 Luck points when their actions contribute to restoring order.
Culture: Characters whose Goal is Culture gain 1D6 Luck points when their actions contribute to cultural preservation and/or education.
Health: Characters whose Goal is Health gain 1D6 Luck points when their actions contribute to improving health conditions for a community.
Prosperity: Characters whose Goal is Prosperity gain 1D6 Luck points when their actions contribute to improving the economic wellbeing of a struggling or impoverished community.
Exploration: Characters whose Goal is Exploration gain 1D6 Luck points when their actions contribute to the discovery of strange new worlds and new civilizations.
Science: Characters whose Goal is Science gain 1D6 Luck points when they participate in scientific discoveries.
Investigation: Characters whose Goal is Investigation gain 1D6 Luck points when they participate in successful investigations involving research, interviews, detection, etc.
Recreation: Characters whose Goal is Recreation gain 1D6 Luck points when they successfully apply their expertise in various forms of recreation to a mission-related task.
Hobby: Characters whose Goal is Hobby gain 1D6 luck points when they successfully apply their expertise in a hobby to a mission-related task.
Career Advancement
Career advancement is marked not by Luck, but by promotion in rank and/or asssignment to various positions and/or ships, starbases, etc. This is based on the crewmember's performance, the judgement of superiors, the nature of the organization, and sometimes outside influences of one form or another.