Sphere of Influence Achievement

Around level 3-5 you'll receive a quest from your capital to visit another player's Ambassador and finish their quest. Once you receive that quest, simply head to a friend's city, or right click on anyone in the chat box and hit "View Empire" and then "Visit" in the bottom left hand corner of the box. Once you're in their Capital you should see the blue "!" on the map/screen. Accept and complete the quest for the achievement.