To invite a player into the alliance, all you need to do is enter the player’s (account) name. If the player is already a member of another alliance, they will have to quit their alliance first before they can join yours.
However, the invitation (unless you withdraw it) will be waiting for them in the player’s embassy. Therefore, beneath the invitation option, you will also be provided with a list of all invited players who have not yet accepted their invite. Within this list, you have the possibility of withdrawing invitations you’ve previously sent: