There are two ways to create a project: create it out of a deal you won or go to Projects tab and hit the big + button.
Give your project a name and set it up as a client project or internal project. If it's a client project, you need to put down a company you're doing this project for.
Choose a company from a drop down menu. If you don't have it yet, start typing the name and create the company now.
Hit the Create project button and you're all set.
Private vs. Public projects
When creating a new project decide whether it's a public project or a private project.
Public projects are visible to everybody in your company and everyone can join in.
Private projects are the ones only managers and admins can join and then they can invite other people as well.
Be aware of the change this causes in time tracking - people won’t be able to track time for projects they are not members of. Productive will ask them to join a project before they can track time against that project’s budget.
If you want to turn an existing private project into a public project, go to the project menu...
… and select Edit project option.
Time on tasks
This is a feature you can use for tasks in a project if you want your team members to track their time directly on each task.
You can read more about it here.