Although battles are your bread and butter they are not as exciting as you might want them to be. You can see how a battle goes but you don't have much influence on its result. Space battles are rather simplistic. First, you must force your enemy to stop in a system by using the blockade order (the one with the symbol of a shield). If enemy's fleet is still in a system select attack icon (crossed swords). You can now see an initial battle screen. Here you can make some preparations. After selecting a tactic and placing your units you can proceed with battle. You don't have any direct control over your fleet during a battle but you can do a few things that will grant you victory.
Before a battle you can choose which ships belong to one of the three striking teams: flanks and center. Place your ships while keeping in mind your tactic, range and weaponry of your fleet.
Choose the right tactic. You can choose from a few tactic cards. They are special behaviors for your ships during a battle. The cards inform you about two things. First, you can see a default placement of your fleet. Second, you can check bonuses for your entire fleet, e.g. better defense against projectiles or stronger shields. If you have a lot of ships that are equipped with weapons that are good at close distance you can select a suitable tactic that allows you to get closer. Your fleet is armed mostly with missiles? Select a tactic in which your ships will stay away from your enemy.
Appointing an admiral as a commander of a fleet can also help you to win. However, you must assign him to a group before a battle takes place. His ship is not counted in the Command Points of a fleet and, usually, he is very useful especially in the beginning of the game. It is best when a hero has at least one or more abilities that can help your fleet. Assigning a hero with an ability that increases attack of laser weapons means nothing if your ships use kinetic weapons.
The easiest solution for winning a battle is to: have a few fleets (they can finish of a wounded enemy), have a more numerous fleet (more means better - your armies receive a small attack bonus; however, you need more Command Points), bigger ships in your fleets (a medium ship requires 3 Command Points which can be converted into 3 small ships; its firepower is simply higher than that of a group of small ships) and installing better weapon and defense modules in your ships.