Your ship’s power is one of the core things in Star Trek. If you don’t have any power, you can do nothing at all, and no matter how much power your Warp Core can provide, it’s never enough. You have to distribute power to the subsystems of you ship depending on your current needs.
All of the systems on a ships are divided into 4 groups of Subsystems: Weapons, Shields, Engine, and Auxiliary. Increasing power to weapons, shields or engines will boost the performance of them respectively: for example, having 100 power in weapons will increase your damage output, while having 100 power in shields will increase its regeneration rate. Giving more power to auxiliary systems will increase the effectiveness of your Deflector Array, Tractor Beam, Ship Emitters, Sensors and similar which is used by certain abilities. Auxiliary power will also increases your ship turn rate.
On every ship you have 200 units of power which can be distributed however you like. You must allocate at least 25 power units to a particular system and a maximum of 100, meaning you can have all 4 subsystems at 50; or 1 at 100, one on 50 and other two on 25.
When you begin the game you have 4 default power presets set by default. One is for Attack (100/50/25/25) and it’s probably the one you’ll be using the most. The second preset is for Defense, having 50 power in weapons and 100 in shields. The third is for Speed, with 25 power in weapons and shields and 100 in engines. The fourth preset is “Balanced” but hardly so: I doubt you’ll be using it much unless you rely a lot on your engines and abilities. It might come in handy when in large groups so don’t dismiss it entirely though.
You can quickly change from one power preset to another by pressing the small icons as displayed on the image above. Note that the power will not be diverted immediately, but rather take a few seconds so keep that in mind as well. By pressing the fifth icon () you can set custom power profiles as well.
The maximum ship power is not set in stone however and you can increase it to over 200. Escort ships can have 110 power in weapons and Science ships can have 110 units in auxiliary power. Cruiser ships have a +3 units bonus to all systems. You can also increase power by using certain types of consoles which give power bonuses. Additionally, if you carefully look at your skill points you’ll notice several skills which allow you to get more power from your ship’s Warp Core. There are several efficiency skills which make certain subsystems more efficient at lower power levels (less than 60), and performance skills which make them more efficient at higher power levels (60 units or more).
There’s also the Warp Core Theorist trait available when you create your character which is one of the best ones you can take: if you don’t have it though, don’t go delete your character because of it. While it’s highly useful, it’s not mandatory in any way.
Be sure to familiarize yourself with power levels and presets and be ready to change them during combat! If you run into several enemy ships while your allies are lagging behind always switch to defense preset to buy yourself some time: it helps A LOT. Don’t forget about the Speed preset either: while the game is very forgiving when it comes to dying, sometimes it might be better to escape the battle and let your allies take the heat for awhile, especially in PvP. As I already said though, most of the time you will be running with Attack preset, but switching to another in the right time is what differentiates good captains from great captains.