Steps
Open Settings → Users & Roles, on the Team tab.
Choose Invite someone.
Enter their email address.
Choose their tier and tick their roles.
Add a message if you like.
Choose Send invitation.

What they get
An email with a link to join. If email isn't set up, use Show link to copy the link and send it yourself. Resend email sends it again; Revoke cancels it.
Good to know
The invitation is matched to the person's verified email address when they sign in, so it can't be used by someone else.
You can only give roles whose permissions you hold yourself.
Remember to give them workflow roles too, or they won't be able to move anything on the boards.