Gaining Honor in Empires and Allies is really simple! Similar to CityVille, FarmVille, or any of the other Zynga games, you will see blank portraits at the bottom of your screen and an "Invite Friend" button. Click one and the send an invite to individual members of your friends list to join the game. Once they accept the invite, their portrait will replace the blank ones that once were there. Click on any friend's portrait, and you will be prompted to "Invade" or "Visit" them.
You gain Honor by visiting other friends and helping their army grow, whether by collecting rent from homes, speeding up farms, accelerating oil refineries, or by lawn mowing trees (ok, not really, but you get my point). Your friends' bases will have small portraits above each area you can help with, and you have a separate five Energy to use for each friend you visit. Use this energy to gain money, lumber, or oil as well as Honor. Honor drops as red hearts in place of the blue stars for experience. You gain levels for reaching certain amounts of Honor, and your Honor level is displayed beside your portrait on your friends' displays. Battle on!