I'm actually getting some suggestions from the FP community so I can build my own reputation system on my website.
Typically, forum reputations work in such a way that users can influence, plus or minus, the reputation of other users on posts they make. Users start off with 0 points of power... and they get a point of reputation influence power for every configured milestone they reach (usually things like making 1,000 posts, or being a member for several months, and so on). When a user gives another user reputation, plus or minus, the number of reputation points that user gains or loses depends on the reputation power of the user who gave the reputation. Many forums also pose limits... eg. you can only give X reputations per day... you can't give the same user reputation again until you gave X other users reputation... and so on.
The nice thing about the above system is that reputation is in the hands of the users, and it requires little to no staff maintenance. Plus, with reputation influence being determined by how well established a user is by things such as membership time and number of posts made, more established users are more trusted and thus can influence reputations more strongly. And the reputation limits help prevent abuse.
However, there is a major downside. A reputation system like this encourages favouritism. Users on social media tend not to use reputation for what it really is supposed to be for. Instead, they use it as a method to award users they like, and punish users they don't like. So someone on FP actually recvommended to me that the power to take away reputation should not be in the hands of the users. In other words, users should only be able to add reputation, not take reputation away. And only staff should have the power to take reputation away. This makes the reputation system less abusive, but puts a little more work on staff. I however think it's a good idea for a reputation system to operate in that regard though. And perhaps you can make more incentives, such as giving users perks for reaching certain levels of reputation.