The following actions will reward you with experience:

• Building a new Module
• Upgrading a Module to a new rank
• Attaching a higher-level weapon / shield / armor to your Modules
• Collected blueprints
• All Research except Mk upgrade research

The following will not result in a base experience gain:

• Banking resources
• Destroying VEGA / Enemy Fleets
• Destroying a player's base
• Building a new ship
• Refitting a ship with different components

Also, when you downgrade during a refit or scrap something in the game you will not gain experience again until you rebuild up to the experience in which you just downgraded or scrapped. As a note, because there is a limited amount of blueprints, modules and research this does mean there is a "level cap" on bases that will only increase as new content is added. I hope this helps explain things better!