Atlas Reactor is a fun and innovative game. That's generally a good thing, but the danger of innovative games is that they'll confuse people and then get ignored. So I'm here to help with that.
Battles are between two teams of four. Combat is strictly turn-based, and play continues for 20 turns or until one side takes 5 deaths, whichever comes first. If the game is tied after 20 turns, it goes into sudden death, and the next turn to end with a non-tied score ends the game.
You get eight skills. On each turn, you can use exactly one skill. The exception is that a relative handful of skills are labeled as a "free action", meaning that you can use it in addition to another skill on your turn. Five of your skills are determined by your freelancer (i.e., the character you play as), and the other three are catalysts that are the same for all characters.
Turns are divided into four phases: prep, dash, blast, and move. Every skill is labeled as being a prep, dash, or blast phase skill. Each skill takes place in the phase that it is labeled as. You can use one skill per turn, not one per phase. All skills used in the same phase are considered to be simultaneous, though the game usually displays them as happening one at a time for clarity and dramatic effect. Skills used in different phases of the same turn are not simultaneous, but take effect in the order that the phases occur.
The prep phase is for buffs and debuffs. You cannot move during the prep phase, nor can you deal or take damage. Healing and shields commonly occur during the prep phase, and this precedes taking damage, so they can mitigate damage that you take in that same turn.
All dash phase skills involve moving the character. Some also deal damage, but many only move you.
The blast phase is where most damage is done. Skills that do damage and nothing else are blast phase skills.
The move phase is the final phase of a turn. Any character who did not use a dash phase skill to move during the dash phase can move during the move phase, even if he used a prep or blast phase skill. A player who did not use any skill at all can move twice as far during the move phase.
Importantly, your skill use and movement for a turn must be decided before any of the phases play out. You have to decide where you will move in the move phase before you see who deals how much damage in that turn.
In particular, you have to decide if and where you will attack in the blast phase before you can see if and where your opponents will move during the dash phase. The point of most dash phase skills is to get out of the way of an attack that is coming in the blast phase, though you also have to choose your dash phase skill use before seeing if and where your opponents will attack.
Your movement choices for the move phase can be modified if skills used in other phases knock you back or root you. Your movement may also be diminished by skills that slow you, so for example, if you wanted to run 5 squares, but a skill slowed you during that turn, you might only move the first three and stop.
As I said above, you have eight skills. Your first skill depends on your freelancer is always a blast phase skill that deals modest damage. It is special in that it is your only skill with no cooldown, so you can use it every single turn, or perhaps rather, every turn that you don't want to use some other skill.
Your next three skills also depend on your freelancer, and can be in any phase. The details vary wildly from one freelancer to another, but they generally have a cooldown of some number of turns. So for example, if you use a particular skill, you can't use that same skill again until four turns later.
Your fifth skill is your ultimate skill. It tends to deal heavy damage and doesn't have a formal cooldown, but you can't use it until you have filled your energy bar. You gain 5 energy per turn, plus additional from using various skills. This typically lets you use your ultimate skill once or twice per match.
Your final three skills are catalysts. Each catalyst slot has two or three options, so you get to pick which catalyst is loaded for each catalyst skill slot, but this has to be decided before the match begins. They are the same options for each freelancer. Each catalyst skill can only be used once per match. It's available right from the start, but once you use a catalyst, it's gone for the rest of the match.
Above, I said that all skills in a given phase are simultaneous. This can result in characters killing each other in the blast phase. For example, if we each have 10 health and each choose a damage that will deal 20 damage to each other, I might shoot you first and empty your health bar, but then you'll still have the opportunity to shoot me back and empty mine. The game won't show either of us as dead until we both get to play out our turns.
Continuing the example, if someone else heals you for 15 during the blast phase, that can save your life. It might show me bringing your health to zero before the heal, then the 15 heal bringing you back up to 5 health, and then you live. Or it might show the heal first to bring you to 25, then my damage brings you down to 5 health. The results are the same either way, and again, it's all considered simultaneous.
The game does sometimes show a player as dying during the blast phase without waiting for the phase to end. It won't do this until all actions involving the player have played out--including the player's use of his own skill, if applicable.
There are several places on the map where power-ups spawn after four turns. Lights on the square show the progress toward the power-up spawning. These can be claimed by either side, and you can also pick up a power-up by moving across the square without stopping on it.
Many skills can have their damage halved by cover. If I'm standing at a short wall and you're some ways away and shoot me over that wall, I probably only take half of the normal damage because the wall provided cover. Corners of tall obstacles have this effect, too. Not all skills have their damage reduced by cover, and cover doesn't have any effect if opponents are on adjacent squares.
There are also line-of-sight considerations. Some squares on the map provide stealth, and you can also get out of the line of sight of your opponents, at which point, they don't know where you are. The game will show them the last position at which they could see you. Using a skill breaks stealth, but only tells your opponents where you are if you're in their line of sight.