The documentation here is intended to show you how to use MegaMek's interface. Information on the rules of BattleTech is intentionally left out. There are several introductory guides on the Internet, and of course you're encouraged to buy the BattleTech sourcebooks to learn about the game.
When you start MegaMek, you'll be presented with the Main Menu. A game will begin in the Lobby, proceed to Deployment, and then cycle through the Movement, Weapons Fire, Physical Attacks, and End/Heat phases. When only one side remains, there will be an end-of-game report and then the players will begin again in the Lobby.