You need to send another Constructor to that base, upon reach a popup will let you add one module. What modules you can add depends on the techs you have already researched, some "yellow" techs enable you new influence-increasing modules on Influencer Starbases.
Factory techs unlock planetary enhancing modules on EconStarbases, as well as Freighter-income can be increased.
On Military Starbases you can add ship-support modules, such as increased speed or attack/defense. This is research by the "Starbase Defenses - Starbase Conquest Strategy" branch of the tree, as well as all 3 red weapon-branches.
Generally you can add some additional Att + Def on all 3 (4 if you count Resource Starbases as well) of these above mentioned bases, by researching "Starbase Fortifications" brach.
Lots of folks generally abandon most bases because of their inefficiency, but they can be plenty of fun to manage also. If you're going for them you might want to get some upgrade in Miniaturization-techs and built Tiny Constructors solely.
Possible suggestions for these bases would be
to set up an Über-research/prod-system with a ring of EconStarbases in a system with decent tiles
flipping allied planets by building Influencer Bases *directly* at these planets
setting up a web of Military Starbases and lurring the enemy fleets there by having an empty planet or a ship with special-module equipped, and trashing them to dust with the sheer force of your Tiny Fighter Starbase-swarm. This I like most 

