Admin: you need to go to Users (left menu) → select a user → Edit user (gear icon on top) and check/uncheck the Has admin privileges option.
Project manager: you need to go to Users → select a user → Projects tab → Assign projects, then select the desired projects and check the option to set the user as project manager.
If you click on Edit user, you are able to give the project manager more privileges like adding projects, invoices, estimates and expenses.
Regular user: you need to go to Users → select a user → Edit user and allow them to add projects or to manage expenses, estimates and invoices.
If the user creates a project, they will be able to manage that project, including assigning users, checking their timesheets, setting the billing rates, etc.
NOTE: Project managers/regular users with the Can manage invoices right will be able to see the billing rates and invoice unbilled AR of the project.