There are a couple ways to send a guild invitation. You must have inviter, leader, or founder rights to be able to send a guild invitation.
1. Click the global button (lower left corner), then the guild button (middle of pop up window). Choose the administration tab and type the players name into the box to send them an invite.
2. Find the player you wish to find in the global rankings [Global button, global rankings button (left button on pop up window)], then find the player you want to invite either by scrolling or by doing a search on their name, then choose the invite player to guild button on the far right of that player's listing in the global ranking list.