I don't know if anyone's explained how actions and maneuvers work in combat, so I'll take a crack at it. If I'm repeating something or telling you something you already know, then I'm sorry :p As far as how turns go, you basically get 1 Action and up to 2 Maneuvers per turn. The action is used for the big things, similar to D&D, like Attacking or grappling someone or operating a computer. Maneuvers are for little beneficial things like moving, aiming, taking cover, etc.
As far as Maneuvers go, I said that you get up to 2, but only one of them is actually free. If you want to use the 2nd one, you have to suffer 2 Strain (if you take so much Strain that you meet your Strain Threshold, you pass out). When you use a maneuver to move, you move in "range bands." So instead of calculating the exact feet away from an enemy, we say we are at "short range" or "medium range." So one maneuver to move will move you one range band (in most cases) closer or further away from the enemy.
Aiming is a really useful maneuver, especially if Xin isn't great at shooting things yet. You can aim up to 2 times consecutively in order to add a Boost (blue) die for each time you aim. So you can aim once and shoot, or if you want to take 2 Strain to get a 2nd maneuver, you can aim twice and then shoot, giving you two Boost die (which is what Bast did on his action).
When you attack with a melee weapon, the difficulty is always a base of 2 purple dice. Sometimes this can be different, depending on if they have defense or if they're a really tough boss-guy. When you're shooting at someone the difficulty depends on the range. At short range the difficulty is only 1 die by default. Medium is 2. Long is 3. Extreme range is 4. Shooting while engaged (in melee) is another thing that, hopefully, you won't have to deal with.
If you succeed, you take your weapon's damage and you add your excess successes to it for the total. Some weapons have qualities you can activate with your advantages, but otherwise you can spend them to give other people boost dice or upgrade their checks. Preferably you can get a critical hit with them. The number of advantages you need to score a critical hit is determined by the weapon's Crit score, so lower is better. Xin's blaster pistol has a 3 Crit, so you can spend 3 advantages to do that.
Hopefully this helps!