To play the metaverse you first need to create a character, which I see that you've already done. You can create up to 3 different metaverse characters per user id. When you start a metaverse game you're given the choice as to which character to use to play the game.
Starting a metaverse game is pretty much the same as starting a regular game except that instead of pressing the "New Game" button from the main menu you instead press the "Metaverse" button.
However unlike a regular game when you start a metaverse game you have to be connected to the Internet because the first thing you need to do is to log in to your Stardock account. This is done directly through the game. You'll get the "Metaverse Log In" window and you'll need to enter in the same User ID (i.e. Nickname) and Password that you use to log in to the forums.
Once logged on to the Metaverse the "Play Metaverse Game" screen will be displayed which gives you the chance to select the character you want to use if you have more than one. This screen also displays a few statistics about the metaverse games that you've played so far as well as provides the "create character" and "metaverse manager" buttons both of which open up your browser to the metaverse home page.
So once you've selected the character that you wish to play then you press the "Play" button which brings you to the same "Galaxy Setup" screen that you use to configure a regular game. From here on out everything else is identical to a "regular" game.
Once you've created a metaverse game then you play just like normal and can save and reload the game without having to be connected to the Internet. The only time you need to be connected to the Internet is when you start the game and then again when you end the game and want to post the score to the metaverse. Otherwise everything is just like a "normal" game.
You don't actually play with others in the Metaverse, all you're doing is playing a single player game whose results are essentially stored in what amounts to a high scores list.
You can have your characters join an empire and if you have multiple charaters you can have each of them join a different (or the same) empire. To join an empire you need to go to the empire's metaverse home page. The easiest way to do this is to go to the Metaverse home page and press the "High Scores" button. From there you can view the "Top Empires" list (http://metaverse.galciv2.com/index.aspx?g=topempires) and clicking on any of the empires listed (click on the More button to see the complete list) brings you to that empires home page where you'll see a "Join Empire" button that you can use to join that specific empire.
To create an empire of your own go to the Metaverse home page (http://metaverse.galciv2.com/) and select the "Edit my Empire" item from under the "Account" menu. From there you'll get to the Manage Empire screen which allows you to create and manage your own empire.