The process is basically same regardless of the mode that you choose. When you select you opponent, you can see brief enemy status. The thing is, this information doesn't show you the result. It is only about the scale, so even if the indicator says your army is inferior than the enemy, you can still win if you have better equipment and better upgrades.(Nevertheless, it is not recommended to fight if you see the indicator almost filled with a red bar.) In the Alien raid mode, you can see remain health of the Alien fleet instead of the indicator.
Just before you go out to the battle field, you can organize your fleets. You can set the fleet formation and refill your units to maximize the battle efficiency.
After all the process, you can see your fleets fighting. There is a special engage rule in this game.
Battle process : Buffs activated -> Long range weapons' turn (Cannon fire -> Missile fire -> Cannon fire -> Missile fire) -> Short range weapon's turn(Beam-> Fighter -> Beam ->Fighter -> Beam -> fighter)
As you can see, long range weapon ships can shoot first, so they can reduce short range weapon ships' combat performance before the short range combats. In short range, long range weapon ships don't fire anymore, so they become totally nothing more than tankers. Thanks to the late turn, short range ships can damage enemy fleets more fatally. They have higher firepower and one more turn to attack, so if your long range weapon ships failed to reduce those ships' number in advance, it could be a disastic combat situation. After all, you win if you destroy more than 50% of enemy's fleets first. If you failed to achieve the victory condition or take 50% of your fleet losses first, you lose.(Even though your fleets have potential to win with extra turns, it doesn't change the result.) You can skipped the scene if you want, but it is recommended to watch it when you are looking for a specialized strategy against specific types of enemies. Every weapons have their own pros and cons, so check the pages to make your fleets efficient.
Finally, after the fight, you can see the result screens that reports how well your fleets fought and what rewards you gained.
Also, you can be attacked by someone when you are not playing the game just in the same way. If your fleets lose continuously, you will be protected by a shield for several hours automatically. During its activation, you can't be a target of enemy nations, but if you attack others or the shield is expired, you can be attacked by your enemies again.