Using Open Project, how can one calculate time spent on a project by resource?
Given 5 people, I'd like to know how much time each person is spending on the project.
Is it done manually, or can we get a report covering this?
You are probably looking for a time sheet management system where users enter the time they have actually spend on each project. Please search Google for "open source time sheet management" for a selection of available tools. You might also want to search for "open source openproj integration" in order to find a subset of these tools that actually have an integration interface with OpenProj (or ProjectLibre, as the latest version is called).
The two system work together as follows: After creating your project schedule in OpenProj, you import the schedule into the time sheet management system. Once your team members enter their hours, you can compare task advance vs. resource consumption vs. time spent.