I've researched the Gateway tech, but I can't use the existing gateways - neither science ships nor construction ships can do anything with them. It says the gateway must be upgraded before use. How may I do that?
The Gateway needs to be in your territory for you to be able to activate it. To get it activated again, you need to click on the Gateway and click the upgrade button. It costs 10,000 energy and 5,000 minerals. Gateways (as you probably know) allows connection to other gateways across the galaxy. See the gateway section here.