There are several ways to get research points:

• Each tick your empire will produce 1 Research Point.
• You gain 1 research point every time you build a Metropolis
• You gain 3 research points every time you build an Orbital Ring
• You loose 3 research points every time you demolish an Orbital Ring

Once you have accrued enough points you can choose to spend them to advance your empire. All advances are detailed into the Research tab.