Basics - Home Screen

Home Screen - Heroes Screen - Battle Screen

Home screen, what you see when you first log in.

Upon logging in you will be presented with the home screen. It shows your currently equipped party deck of heroes as well as everything else you need to know:

From left to right at the top of the screen:
Equipped hero - You can equip a hero that provides a small buff to your party. The equipped hero must be in the party for the buff to be active. Any ongoing events will show up under here.
Stamina - Your stamina is represented by the lightning bolt icon. Stamina is used for missions. It replenishes at a rate of 1 stamina every 10 minutes. Every level up increases your max stamina by 1.
Energy - Right next to the stamina is your energy, represented by the green battery icon. Energy is used for Boss Raids, the Dungeon, Time Attack, and the Arena. It also replenishes at a rate of 1 energy every 10 minutes. Every level up increases your max energy by 1, up to a maximum of 30 energy.
Gold - Earned in a variety of ways, gold is used for upgrading heroes, reviving fallen heroes, or increasing the number of heroes you can hold by expanding hero slots.
Carats - The "premium" currency of the game, carats are used in the shop for purchasing heroes, boosts, and other goodies. You may purchase carats with real money, but at the same time you can gain many carats from simply playing the game.
Honor - Honor is the last currency you have. Honor is used in the honor section of the shop to purchase heroes or items. It is obtained from friends and participating in the Arena. You can increase your max honor by 5 from "mastering" heroes, leveling them up to level 30. Heroes that have already been mastered once will not increase your max honor if you master them a second time.

Buttons at the bottom of the screen:
FAQ - Opens a window that takes you to the game's Frequently Asked Questions section.
Options - The options menu. Pretty self-explanatory.
Friends - From here you can send or accept friend requests, send and receive honor points. as well as check on your friends' heroes. You also have the option to send invites to your Facebook friends for rewards.
Messages - Your inbox and gift box. Messages sent to you will show here. You will also receive bonuses and other rewards here.
Shop - Here is where you will spend carats and honor points. Where you may get an awesome legendary hero or a measly common. This is where rollercoasters of emotions happen.
Recruit - This button brings up basically a glossary of all available heroes in the game. Very useful.
Quests(1)  - Shows your progress on your quests, which are basically milestone achievements. Provides you will gold, honor, and carat rewards.
Carat Mine - The unnamed button. For your efforts in combating the evil forces, you have slaves mining in the carat mine. Gives you 1 carat when the timer reaches zero. Timer starts off at 12 hours for 1 carat, but leveling up eventually lowers the timer by 20 minutes per level.
Heroes - Takes you to the hero management screen where you can equip, upgrade, train, and fuse heroes.
Quests(2) - The daily quests. Separate from the other quests, this button brings up the daily quest. Completing 7 daily quests in a row will reward you with 10 carats.
Start Battle - This button brings you to the battle screen, where you can then choose to do missions, boss raids, dungeons, etc.