Try starting as the Humans on an easy setting. A medium map would be my recommendation. Choose 2 or 3 opponents.
Click on your colony ship and then right click Earth. That'll put your colony ship in orbit. Relaunch your colony ship and choose the maximum amount of colonists. This will be 250 for DA or 500 for DL IIRC.
Click your colony ship and right click your secondary planet (Mars). That'll send the colony ship to that planet. Congratulations! You just became an interplanetary power.
On Mars, put a factory in the queue. Leave it to its own devices for now.
Go back to Earth. Put a factory in its queue and then click on "buy". You want to do that because just buying it without putting it in the queue costs a LOT more.
Put two more factories in Earth's queue, followed by one lab and one economy structure. (I don't recall what the lower level econ structure is, but it looks sort of like a folded wallet).
If you have a miner, double click it and set it to "automate" and then forget about it for now. If you don't have a miner, you can forget about it immediately.
Double click your flagship. Set it to Auto Survey. Now, you can forget about it too. As it finds goodies, it'll tell you.
Go to Earth and put a Colony Ship in the queue. Click on Purchase or Buy to rush buy one.
Go to the research screen and select the path to Impulse Drive (light blue). You'll want one of those as soon as you can. Later, you'll want the yellow techs, too.
End the turn.
Launch your new Colony ship and aim it toward a planet that has a class of 8 or above. If you don't see a planet that matches that, send the colony ship out into space blindly. It'll likely find something out there.
Buy another factory on Earth and another colony ship.
Explore and colonize. That should get you started.
More advanced stuff can be learned as you go along. Start thinking about custom ship designs (bigger engines, weapons, etc.). Keep diplomacy and morale in mind. You'll need to choose how you want the game to progress and the techs you choose will help you guide it the way you want.
Don't over extend yourself. Keep an eye on the economy. That's a major part of your empire's success.
Don't be quick to go to war. The enemy will declare on you quickly enough. Just have a plan to be ready to respond. The first time they declare war on you, they'll still be too weak to back it up. Build up quickly enough and you'll make them reconsider their rash decision.
Good luck and ask again when you have more specific questions.
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