You can invite people into the alliance if you are alliance founder with full rights to the alliance (default for the founder) or the alliance founder has granted you a right to invite people into the alliance. You can invite them by clicking your embassy, then go “to the alliance”. Afterwards click “options” and then select “invite a player into the alliance”. Click OK.
You have to write the name of the player exactly as it is to the “Name” box and confirm by clicking “OK”. If the invitation was sent successfully, the game will show “An invitation has been sent to ….” and the invitation appears to the “invitations” table.
After that if the player accepts the invitation, he will join the alliance.