Required level of access: Org Admin status.
1) Navigate to the Menu, then Setup, find "Orgs" on the left sidebar, and then click on the "Members" section.
2) Click on the blue button, "Invite Staff" to enter the email address of the new user. If the system recognizes it as a new user, it'll display an option to invite the new staff member.
3) Click on that option and then click on the "Invite" button.
Once you've sent the invitation, the new user will receive an email to set up their password. Once they log in, they'll be able to update their first and last name.
** Adding a new user to your Org is not enough for them to be ready to go. They also need their permissions set up as well. To learn how to assign them to all existing projects, to all new projects, and to the mail room and to give them Org Admin status, see this article: Global Permissions.