Starbase assaults are an armada-like attack on other Alliances' starbases. In order to start these, they require Tactical Mandate tokens that you get from from your daily Alliance Unity event (20), and from Alliance Altruism chests (100 per chest), which you open with Rare Cardassian Loot.
Once started, they have a 10 minute timer. You can send up to four ships to these attacks, and if you succeed you steal Plasma from your opponent.
The starbases are their own type of event. They aren't PVP, or Armadas, or anything like that, so for now you need to use officers that specifically say they work on Assaults, such as Kira, or that work on everything.
The Starbase will attack ships in order of power. The first gun on the base hits for more than one billion damage, so no matter how much mitigation you have, the smallest ship will almost certainly die on that first hit. This hits every six rounds, so rounds 1, 7, 13, 19, etc, so these must be killed quickly.
Because we can determine the order the ships will die, we can also change the crews. So the sacrificial ship should have an ability that will last the whole armada, even if its dead. The second crew can be a survival crew, because it'll take a lot of small hits over the next six rounds and the goal would be to absorb as much as possible. Alternately, because you know you're going to get hit a lot that second ship can end up outputting a lot of damage if it has Khan, as it can up its crit quite quickly.