Right click on your planet and select Build -> small space port. The space port builds ships and lets ships drop off/pick up resources.
As you will see, a Constructor can also be built from the planet. You use these to build mines and other things away from your home planet.
Once you have a spaceport up you can access the build order screen from the top bar, and choose what you want it to build. You could also do this by right clicking, but the build order screen is more straightforward.
After your spaceport is built, your basic priorities should be:
1.)Open up your design screen from the top bar, find your small space port design (you can filter to state bases to find it easily), select 'Manually Upgrade Design', and add research labs (called weapons lab, high tech lab, energy lab. Not plants, which are for construction) to your space port. The amount you should add is based on your research capacity, but for a first game there's no point worrying about that. Just add 5 of each. If it asks you whether you want to keep things automated, say yes. Once you have added the labs, you need to tell the base to retrofit to this design. Left click on the base, and select retrofit in the box on the bottom left of the screen. You could also order this retrofit by right clicking, or in the ships and bases screen.
Weapons: get armor then anything you want :)
High Tech: Do what you want. You will need colonization eventually to do what it says on the tin. Other essential techs are Transport Systems, Medical facilities, and Recreational Facilities. Note that you can several build wonders with this tree. They are all very good. If you don't know what to pick, go with the Traders Bazaar at the bottom of the tree. Money :)
Energy:Get Energy Collectors in the Energy research tree. Once you have energy those, you can put them on ships and bases to let them power their systems without burning fuel (as long as they aren't moving). Since fuel is a resource (the one you currently use is called Caslon, mined from gas giants), this will save your economy quite a bit. Further research priorities in the energy tree are shields, construction size increases, and warp tech. Note that you won't be able to research warp tech until you have explored your starting system. Build Exploration ships to do this.
3.) Build 2 or 3 exploration ships at your small space port. Automate them if you want.
4.) Pay off any pirates, if you have them enabled.
5.) Build 1 or 2 constructors, to begin building mining stations at suitable locations in your system. You can see what resources each planet, asteroid etc has by clicking on it. You can only see resources once you have explored them, by scanning them with anything that has a resource scanner on board. At the moment that's your exploration ships. You could put a scanner on your constructor as well if you want...your call.
At this point you will have decent research, the ability to make ships and mining stations, the techs that allow your ships to not blow up instantly when attacks (armor, shields), and the techs that allow you to ferry troops or tourists around, depending on your inclination.
Hope that helps a little.
Edit: Also try the in game tutorials.
< Message edited by Tcby -- 6/20/2014 12:31:51 AM >