In the people section of your project, you can see the current people who are on the project and you can click the 'Add People' button in the top right to add more.
Adding people already invited to the site
In this screen:
You'll be able to view all people already on the site who you can add to the project, you can search for a specific name or you can filter by role to narrow down the list of people who are listed. People who are users will show as green and contacts will show up with blue.
You can click to select/deselect them individually, and you can use the 'Select All' and 'Select None' options at the bottom to bulk select/deselect. When you select someone, you'll see a green tick icon to the top left of their profile image.
You can choose to include people who are already on the project by enabling the switch under the list, too.
Once you're happy with your selection, you can use the green button to add the people you've selected to the project.
Adding people who aren't already on the site
You can use the 'Add N' button at the top to add new users to your site and your project in one go. You'll see the screen to add all of their new user details, you can choose to send them an invite to the site, then they'll be added to the list so you can select to add them to this project.
You can also use the 'Add New Contact' button to create a new contact in the site and add them to the project, too.
Adding people from the 'Overview' section of a project
You can add users to a project from the 'Overview' section of a project by clicking 'Options' at the upper-right, and choosing 'Add People' from the menu.
You can then add and invite new users who aren't on the site, or add existing users to the project.