Similarly to After Effects, Premiere Pro, Final Cut and other such programs, Softimage works with a project-based folder structure used to contain the project files themselves and all the necessary assets that go along with it (textures, scenes, audio, renders, etc.). Fortunately Softimage creates this folder structure automatically when a new project is created, so half of the organization is already done for us!
File > New Project brings up the above dialogue box, asking simply for a name and location for the new project.
The Open Projects menu contains a list of all recently accessed projects (including Softimage's preset scenes and samples that come bundled with the software), allowing you to hop back and forth between projects and open different assets from each. As more and more project files are created and accessed, the list on the right can grow to astronomical proportions, so fortunately Softimage's "Project Manager" can help us to manage and clean it up a bit.
You can add or remove projects from the list at your leisure. This won't physically remove them from your hard drive, it will simply add or remove them from the list for quick access. It's probably worth going through and doing a bit of housekeeping to remove complete or deprecated projects from the list every now and again, to keep things tidy.