Its very complicated, but the tldr is its basically like FTL mixed with SF1E starship combat.
Here's the full text, I'll post each page as a comment.
HOW TO USE THIS CHAPTER
The new rules presented in this section show GMs and players how to use tactical starship encounters: how players can customize their battle stations and helm them during encounters, how the action plays out, what characters can do on their turns, what happens when starships take damage, and so on. These rules are divided into the following sections.
TACTICAL STARSHIP RULES
Each round of a tactical starship encounter plays out much like a round of any other combat encounter, with the addition of enemy starships and space hazards represented on a sensor map. PCs move around their starship and helm battle stations to overcome these challenges. This section contains the new rules and tools that players and GMs need to run these encounters. It also includes tips for how each class can approach tactical starship combat, from their choice of actions to the upgrades they select to customize their battle stations. Finally, it includes an example of play to show how a typical tactical starship combat might play out at your table.
Tactical starship combat blends the round-by-round action of a typical Starfinder encounter with strategic starship-scale space battles. These encounters place the PCs aboard their very own customized starship, where they can helm battle stations to control the vessel, overcome hazards, battle enemies, and keep their starship in good working order.
Tactical starship combat works like any other combat encounter. The focus for these encounters remains on the PCs, with the map showing where they are on their starship. PCs roll initiative, take three actions per turn, move their characters on a battle map, cast spells, fire weapons, and use feats, skills, and class abilities to interact with enemies, whether they're boarding the PCs' starship or piloting their own starships within scanner range. If you want to place players at the helm of a unique vessel that levels up along with their characters and allows them to engage in tactical space battles, this subsystem is an excellent inclusion in your Starfinder campaign.
BATTLE STATIONS
This section describes the different battle stations present on most starships, such as the pilot's console, gunnery, and generator. The location of a battle station is indicated on the map you use to represent the players' starship. Using a battle station is as simple as moving to it (or beginning in its square) and using its station actions. Any character can helm any battle station.
Starship Equipment
Battle stations grant a core set of actions and benefits, and players can customize their battle stations to suit their characters' needs. For example, a crew might install upgrades in a gunnery empowering the solaran to blast enemy starships with their solar flare. A different crew might select an upgrade for their starship's magic conduit that allows a witchwarper to Warp Reality in space. The gunnery can be equipped with a wide variety of weapons. Starship expansion bays add to a starship's capabilities during exploration and downtime.
Advancing Starships
As the party advances in level, so does the crew's starship. This section provides three base frames for player starships. The frame determines their ship's Speed, Hit Points, Armor Class, and so on, just like a character's class determines many of their statistics. As characters level up, their starship's statistics improve based on its frame. Only two player starships might have similar default statistics based on its frame, but the selection of upgrades makes each ship unique!
GM'S ARSENAL
Additional information about tactical starship combat for GMs, including advice for running a campaign with starships, building and balancing tactical starship encounters, and a plethora of enemy starship and space hazard stat blocks, can be found starting on page 201.