How do you make an alliance with another guild?

im so stupid, but how do you do it?

I'm not the leader of my guild so I'm guessing, but the option should be on the Alliance tab of your Guild window. Before you can ally with other guilds, however, you need to ally with either the Kurzicks or the Luxons, since alliances are only permitted between guilds linked to the same faction. You can do that by talking to the NPC marked [Allegiance] in House zu Heltzer (Kurzick) or Cavalon (Luxon).

Yes, if your guild belongs to the same faction as the guild you wish to join in an alliance, the guild leader sends an alliance request to your guild just like a new member would get invited, except the cost is 1000g instead of 100g.