Best way is to just jump into a sandbox game (in other words not the campaign) and try stuff out.
Fiddle with the knobs. Pull the sliders. Gaze with awe at the flux capacitor. Listen to the noise that the game makes when you press Turn with the brakes on (hmm, that's an idea, I must try that some time).
Ships! Design ships with big guns! Ships with lasers. Ships with missile launchers. Ships with anti-proton gatling cannons (so, more guns). Ships with warp drives! Ships with hyperwarp drives! Whoa! Get pulled over by cops and swear that you weren't doing Transwarp 26 through a Warp 4 zone. Get four penalty points on your license and a fine for 2 billion credits. Harsh.
Take over the galaxy with military force. Laugh maniacally as the peons that oppose you are crushed. Start a new game.
Build lots of research facilities and research the secrets of life the universe and everything. Gaze dumb-founded as all screens blink 42. Ascend to a higher state of being. Start a new game.
Create terrifying weapons of destruction. Find Alderaan (there must be one somewhere in the galaxy!) and test these weapons. Proceed to negotiate with your enemies and then blow up their stars when you no longer need them. But watch out for small fighter squadrons trying to take a crack at those exhaust ports. Start a new game.
Create a set of rules for conducting business. Spread the knowledge of these rules far and wide. Reap the rewards of a huge tourism income as people of all races come to your planets on vacation and buy your merchandise. Become the defacto leader of the galaxy through your influence alone. Start a new game.
Play against the Drengin. Get swarmed by waves and waves of corvettes that maraud around the galaxy looking for a fight. Watch everyone else surrender to the Drengin or get wiped out by them. Be the old race left in the game with a massive sea of red all around you, closing in. Enjoy witty banter with Lord Kona, Start a new game.
Ignore the message that warns you that the Korx have tapped into the power of some precursor relic and will one day become god-like. Wonder why the whole minimap is turning grey then realise too late that the Korx are well on their way to winning. Curse not even knowing who their leader is despite having traded with him during all the previous games. Start a new game.
Panic, loot and flee as the Dread Lords return to reclaim the galaxy. prompting a painstaking search to find out exactly where those guys are. Oops, they've already started cranking out dreadnoughts. Start a new game.
Sigh at the endless expanse of unexplored space. You've played for two game years and yet uncovered just a few percent of the total grid squares. Actually consider designing ships with two engines instead of one to get around faster. Yes, you've been playing on an Immense-size map, and it will take you a while to win. When you do, or you give up because of the huge undertaking that is invading the rest of such a large galaxy, start a new game.
Start an alliance of like-minded races and try to get everybody on board despite the fact that they hate each other, and you as well. Think to yourself, "What would John Sheridan do?" And then the answer will come to you - he'd start a new game. 
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