How do you battle?

To resolve a battle, follow these steps as described in the rulebook:

Beginning with the active player and proceeding in turn order, each player with ships in range of the active region may move any number of those ships to the region to join the battle.
Each player only gets one chance to make this decision.
If the active region is a nebula, only ships with Voyage may join a battle there.

Beginning with the active player and proceeding in turn order, each participating player may play one diplomacy tactics card from their hand and immediately resolve its effects.
Each player only gets one chance to play a diplomacy card.

Each participating player counts how many dice they will roll and determines their targeting value.
If raiders are participating, also count their dice and determine their targeting value.
Beginning with the active player and proceeding in turn order, each player may spend any amount of energy to gain one die per energy spent. Each player only gets one chance to spend energy.
No participant may roll more than 6 total dice.

All participants (including raiders) simultaneously roll their dice.
Each participant rerolls all dice results that are less than their targeting value until each of their dice results are equal to or greater than their targeting value.
Targeting value is the number of ships a participant has in the active region, plus modifiers, up to a maximum of 5.

Each participant compares their highest single die result. If there is a tie, compare the next highest die, and so on.
If a tie is not broken after all dice have been compared, there is no winner and everyone loses.
The winner advances 1 space on the supremacy track and claims any raider reward if applicable.
Each defeated player may take the Tactical Operations action on their station (draw 1 tactics card or gain resources from a slotted moon token).

Defeated ships are damaged according to the battle outcome (details on damage are found on page 24).

Source: Core Rulebook, pages 21–24

Sources:

Rulora