So, you've colonized your nearby planet, next to your homeworld, and you have got some buildings going (I hope there Factories). Have you built any ships? Especially Colony Ships, so that you'll be able to colonize more planets? To do this go to the "build ship" button and from the choices on the right select colony ship, and press build/contruct. I don't remember the exact name. Then if you want to have it by next turn, which in the beginning it's a good idea, then hit the "purchase" button. I think it cost 960bc to rush the contruction for a colony ship. Then hit done.
Next select your flagship, thats the ship next to the colony ship and double left click it. A pop-up will appear with detail stats of the ship, and advanced commands. Select the "Auto Survey" button and hit done. The ship in the next turn will automatically go to the nearest visable anomoly. If none are present then it will say that the ship has not been able to detect any new anomolies, and will return to normal mode. If that's the case then simply move it towards another stay system by looking for the white dots on the mini-map. Survey Ships go faster then colony ships, so it's a good stratagy to use in the beginning to help find habitable planets faster, and so you'll know where to send your colony ships. After doing all this select "Turn".
In the next turn, your colony ship will be finished and ready for launch at your homeplanet. (as the game progresses, your ships could be created in any planet that has a starport, so this is not an all the time thing) Now, select your homeworld/start planet and down near the bottom right of the screen close to the mini-map should be a picto-graph of ships in orbit. Select the colony ship (it should be the only ship in orbit, via the selection choices). Once the colony ship is selected, hit the launch botton which is around the area that you selected the colony ship. Once you click on "launch" a pop-up will appear with a slider, asking you to determine how many colonist do you want to board the colony ship. I recommend anywhere from 250-500 this number is in millions of colonist. Max is 1000 or 1Billion colonist. The colony ship will now appear once you have selected the number you want, via the slider, and it will be ready for you to command. Send it to a nearby star system, and colonize the next habitable planet you see.
For the next several turns, continue this until either you run out of money, or all planets have been captured in your area either by you, or opponents. Once this occurs, begin focusing on building constructors, and building starbases at nearby galactic resources, and continuing to build you planets up. You buget will go negative, but if you build the right balance, do exactly as I said above, then it should recover with in a few months time.
I hope this helps!
As for game length duration, like you said it depends on map size, cpu intelligence, and other factors. Small normal maps take at most an evening to complete, while medium to large galaxies can take upto 4-6 days, and huge to gigantic galaxies could take upto a few weeks, considering you play them constantly each day for at least 3-5 hours. Note that games with less intelligent AI will generally be quicker and easier to win then those with stronger, more intelligent AI.