There are effectively 2 game modes. Campaign mode, and missions, they are entirely separate.
Missions are available from the main menu, they generally consist of a scenario battle with specific goals and specific fleets on both sides. You can refit your fleet before combat if you so choose. Some missions (random battle) have randomly generated fleets, you can try out just about anything this way.
Most of this FAQ is about starting a new campaign.
What ships can I get to start with and which one is the best?The starting ships are Wolf, Lasher, Vigilance, Hound or the Shuttle. The re-start (if you die) ships are Shuttle/Dram/Hound. Which Ship you get depends on the second choice you make for your Characters personal history.
Spoiler
The Wolf (choose 'quartermaster') is often considered the most powerful of the starting ships, but is hard to control. It has initially no PD, a somewhat temperamental shipsystem, and struggles against shielded foes due to its reliance on beams.
The Lasher ('adjutant in the Hegemony Navy') is much more newbie-friendly. It comes with three PD weapons, an easy to figure out system, and has the most flexible mount type (there's a ballistic weapon for nearly every role).
The Vigilance ('helmed a patrol ship') is also a good choice given the right initial skill choices and weapon loadout, but again, probably not something a newbie will be able to figure out.
The Hound ('something else') should be avoided unless you put your initial skill points into unlocking the Frontal Shield Generator hullmod. The first thing you'll want to do is get a wing of Talons to increase your survivability slightly.
The Shuttle (always a choice) is a 'just in case' ship - it says so right in the code - and outside of a bug with a custom character creation plugin, I would only imagine it being used for self-imposed challenges.
How do I get more stuff?You can buy ships, items, weapons, and crew from the Hegemony station (brown). You can also get weapons, ships and items from combat (more later).
How do I pick up 1 item? How do I pick up part of a stack of items?Press shift and left click on the stack, this will pick up one item for each click. Press shift and hold left click a slider will appear and you can select from 1 to 500 (max stack size).
How do I progress further? I'm stuck!This can be a complicated answer, but the short version is that you need to grind small combats with mostly pirate ships (red) until you can afford to expand your fleet and take on larger targets.
What are the different weapon types?There are Energy weapons, Ballistic weapons, Missile weapons.
What are the different damage types?Kinetic: 200% vs Shields, 50% vs Armor
Explosive: 50% vs Shields, 200% vs Armor
Energy:100% vs Shields and Armor
Fragmentation: 25% to shield and Armor but often with Area damage
All weapons do 100% to hull
What are the different slots for on my ship?Blue circles are Energy slots.
Yellow squares are Ballistic weapons
Green squares are Missile slots
Grey multishape are "universal"
The number of shapes (square,circle, etc) represents the size of the slot. 2 medium, 3 is large, 1 is small.
Why is my fleet so slow?Your fleet speed is based on the slowest ship in your fleet + the number of ships in your fleet. The more ships, the more you slow down. This applies to fighter wings as well, but for them the effect can nullified if enough hangar space is available. See "travel speed" in ship stats.
How do I repair my ships?Your ships will automatically repair themselves outside of combat. You must have CREW and SUPPLIES for this to happen. Fighters will only repair if they are in a hangar, if your fleet has no hangar space, your fighters never repair. Additionally, fighters can be repaired in mid combat if you have any ship with a flight deck. You can not currently buy repairs at the station, or anywhere else. It's just a matter of time. You can install a hull mod to cut the time in half, if you are badly damaged.
How does the capture mechanic work? What is boarding? What are marines for?After combat is over you get a wrap up screen, it shows the state of your fleet, and the enemies. If you disabled any ship in the enemy fleet, and you WON the combat as well, you have a chance (say roughly 10%) of being able to board the enemy ship. If this happens you are presented with buttons on the ship, which are, Board/Scrap. If you mouse over the ship, you can see how much crew remains, if it's more than you have marines, you probably don't want to try and board the ship, in which case you can scrap it for salvage. (2:1 Marines:crew is suggested) ALSO: If the enemy surrenders, (surrender is written across the ship), you can board it for NO COST (IE: you won't lose any marines, no matter how much crew they have).
Inventory, what is this stuff for? Why doesn't my inventory ever show 0 units? After combat you will get a chance to loot the dead ships. You can get weapons, fuel and supplies. Currently fuel is not used and is therefore a resource just to sell for credits. Supplies are used by your ships to make repairs. Weapons are rather obviously used on your ships to blow things up. If you go over your maximum you will have increased maintenance cost, if you surpass it by more than 50% you get the risk of having accidents in your fleet. You can of course sell anything you aren't using, if you want.
Who are these other ships?Brown fleets are Hegemony. It is not wise to start a fight early in your progression.
Blue fleets are Tri-Tachyon. Also not wise to start a fight early on with them.
Red fleets are pirates. They start aggro to you, and pretty much everyone else. This is your main fodder early on. Find small single/2-3 ship fleets and cut them up.
Grey fleets are Independents. They start neutral to you and are another possible source of explosions and loot.
How does faction relations work?You start neutral to everyone except the pirates. You can't increase your standing with anyone, but if you attack any faction you lose standing and they will fire at you on site (if they can catch you). The station will trade with you no matter what your standing is, but it can be tricky to get past the fleets nearby if you aggro the Hegemony faction (brown).
I saw some ships do weird things in combat, suddenly becoming faster or teleporting or spewing lightning. What's that all about and how can I do it, too? You probably saw a ship use a special System. Every ship has a System, but they do very different things. What System a ship has is listed in its description, to know what it actually does you have to go to the codex and look it up. Or you can just try it out. To activate a system you have to hit F.