In general ships work exactly the same as individual characters. The players narrate what they’re doing with the ship, how they’re flying it, and where they’re going.
For normal operation all characters are considered to be baseline competent at flying a ship. A Piloting Skill, or similar, is helpful for high stakes, high risk maneuvers.
A Ship Save is a roll for the Ship to avoid bad outcomes from risky choices and circumstances. Roll a d20 and compare to the appropriate Ability. If you roll equal to or lower than the Ability you succeed and avoid the bad outcome.
Roll a Ship Save when the determining factor for success is the Ship’s capabilities. If success depends more on the skill of a character operating the ship, the character should roll a Save instead.
Read about the First Failure principle for more guidance on how to determine who should make a roll.
Your ship’s Shields naturally restores 1 point per Round, or faster by spending Fuel to charge them.
Damaged Modules require supplies, effort, and a week to repair by hand or a day in a suitably equipped settlement.
Hull damage requires a stop at a suitably equipped settlement to be repaired. Usually 6 hours per point of Hull, but advanced facilities may expedite the process.
Under normal circumstances ship weapons are instantly lethal against individual targets, while personal weapons are completely ineffective against ships. If applied cleverly, powerful personal weapons or explosives could bypass this restriction.
The same is true for ships of dramatically different scales. A small ship’s weapons are ineffective or impaired against a capital ship, whereas the capital ship’s armaments are likely to be instantly lethal, or at least enhanced, in return.