Ok, I have a base. Now what?
Click on the Empire link, you will see your new base. Click on the Construction ( 0 ) link.
It will take you to the Construction page for the selected base. There you can build all kinds of avaiable structures like Solar plants, Gas plants, Metal Refineries, Shipyards, etc. Check Help page on Structures for more details.
First, you want to increase your base construction and production capacity, to achieve that build a few Metal Refineries, it will reduce the time to build all the other structures. Check the help page what you need to unlock Robotic Factories, it is highlighted in red, also check Nanobots Factories and Automated Factories. All those structures improve your base production and construction capacities.
To be able to research, build Research Labs, each one will give the base more research points.
All structures need power, area and population. To give more of those you will need the power structures, habitat zone and multilevel plataforms, etc.
You will need defense as well. Click on the Defense tab next to the Structures tab. Only defenses will prevent your base from getting occupied. But a base without fleet can be pillaged (the base economy pillage). To pillage the base owner economy, the aggressor need to occupy the base.
Build shipyards so you can build ships. Level 1 allows you to build Fighters. Check the Techologies and Ships under Help page to see what techs are required to build each ship, for example Fighters require Laser level 1 and Armour level 1.