Your ship has three basic systems that require power in combat: Weapons, Shields, and Engines. You have twelve bars of power that you can allocate between them; each system must have at least one bar of power, and can receive no more than eight. A system's stats are balanced around their performance at four bars of power, which is said to be 100% of its regular performance.

The configuration I have found myself using the most is eight bars in weapons, one in shields, and three in engines. This allows me to hit the enemies as hard as possible, removing threats quickly, while letting me stay maneuverable. Still, the power settings are very adaptable, allowing you to react to changing circumstances.

Diverting power to your weapons will cause their shots to do more damage and fly further.

Be warned about the range, though: your ship's speed is not added to your projectiles', so it's entirely possible for your shots to dissipate before hitting a ship you are chasing if they are traveling quickly enough, even if you're traveling just as quickly as they are.

Your weapons will be the system you most frequently divert full power to. If you know you are going to spend your entire turn very close to your enemy, that is the best time to make sure that your weapons are fully powered.

Diverting more power to your shields will allow them to recharge more quickly, as well as cause them to take less damage in the first place.

The shields are a quirky system. In many ways they are a victim of their own success: because you have such a very large amount of them, you can usually afford to leave them at low power while you spend your energy getting near enemies then killing them.

Be warned that getting hit can prevent your shields from recharging, so you cannot simply recharge-tank all enemy shots: if you're taking heavy damage, you'll be better served by diverting power to the engines and getting clear before spending a few turns recharging your shields.

The more energy is devoted to your engines, the quicker and more maneuverable your ship is. Putting a few extra bars of power into your engines can be the difference between it taking two rounds to make a 180° turn and it taking just one.

Engines are a very important system due to the nature of The Last Federation's combat. With sufficient maneuverability you can dodge particularly damaging shots, and it's often necessary to sink some extra points into the engines to get some pilots for leverage with their race's leaders after the battle; just make sure you don't run into a few missiles in your rush to get them!