The Reputation system is very simple to use and gives lots of great rewards. You can reach the Reputation window by going to your character screen and clicking on the Reputation tab. On the left side you will see a list of reputations that you can work on. Clicking on any of them will display statistics on it. If you click the Status tab you can see how well you are progressing.
Each reputation has five tiers. The first four tiers give you a passive ability (one that you cannot click but is always active). The fifth tier gives you a clickable ability. You can increase in tiers by completing projects and gaining experience. More about projects below.
By clicking on the Contribute tab or any of the empty project slots, you can see a list of projects that are available. You'll also notice 6 slots on the left. The column on the left are your active proejcts and the column on the right are your queued ones. When an active project is complete, the queued one to the right of it will become active.
You'll notice that one slot says Upgrade. This is where you'll find various upgrade projects, including tier upgrades when you've gained enough experience. Clicking on any active project will allow you to contribute to it.
Contribute to Projects
When you click on any of the active projects you will see the list of what is required to complete it. Each project has different requirements. If a project has a blue Contribute button that means you have the items to contribute to it. If it is greyed out that means you do not have the necessary items and need to find them by either buying them or doing missions to get them. If it says Filled, then it has obviously been filled.
Once an entire project has been completely filled the countdown timer will start. When the timer is finished you can collect your reward and the next project in the queue will activate. You can then add a new project to the queue. You can also cancel an active project at any time.