You can grant rights to members of your alliance by clicking your embassy, then go "to the alliance". Afterwards click "options" and then select "assign to position".

Search the name of the player you want to grant rights to in the list which appear. Now choose the rights you want to give him and confirm again by clicking "save":

 The following rights you can give to other alliance members:

• assign to position (Hint: Be careful when assigning this right to another player. Everyone who has it can take your own rights away!)
• kick player
• change alliance description
• alliance diplomacy
• IGMs to every alliance member
• invite a player into the alliance
• manage forums