Your role in combat is about encouraging the crew while taunting enemies into making critical mistakes. A Starship can have only one captain, and a character can assume that role only if it is currently vacant. The captain alone can act in any phase of combat.
As a Captain, you can take any of the following actions during any phase of combat.
DEMAND (Any Phase): You can make a demand of a crew member to try to improve his performance. You grant a +4 bonus to one specific check by succeeding at an Intimidate check (DC = 15 + 2 x your Starship's tier). You must use this action before the associated check is rolled, and you can grant this bonus to an individual character only once per combat. Demand might result in negative consequences if used on NPC's, and you can't make demands of yourself.
ENCOURAGE (Any Phase): You can encourage another member of the crew to give her a bonus to her action. This works like Aid Another, granting a +2 bonus to the check required by a crew action if you succeed at a DC 10 check using the same skill. Alternatively, you can grant the same bonus by succeeding at a Diplomacy check (DC = equals 15 + your Starship's tier). You can't Encourage yourself.
TAUNT (Any Phase, Push): You can use the communications system to broadcast a taunting message to the enemy vessel. You select an enemy vessel and a phase of combat (engineering, helm, or gunnery), and then attempt a Bluff for Intimidate check (DC = 15 + 2 x the enemy Starship's tier). If you are successful, each enemy character acting during the selected phase takes a -2 penalty to all checks for 1d4 rounds; the penalty increases to -4 if the enemy's check is made as part of a push action. Once used against an enemy Starship, regardless of the outcome, taunt can't be used against that Starship again during the same combat.