The USS Cerritos is a support ship for commanders level 36 and above. (Our records list it as an Epic Grade 4 Explorer.) Its Support ability can target your own ships, alliance members or other players. Commanders level 35+ can also unlock it by completing the California Class event every Wednesday. Ten completions (10 weeks) give enough blueprints to build it. Once you finish, the event no longer appears.
Support works on any ship in the same system as your Cerritos. Select the Cerritos from the fleet bar. Then tap Support, or pick a ship in the galaxy viewer first and tap Support. It costs Irvinite. You get Irvinite daily from the Support refinery and from the Second Contact event every Wednesday. Support gives the target ship a base damage increase for a limited time. Completing Cerritos research nodes in the Starships research tree unlocks more benefits. Those benefits depend on the target player's research, not the Cerritos owner's research.
Culver Particles come mainly from the Cerritos Refinery. It can also drop Cerritos Components and Lower Decks officer shards. Refinery tokens come from the weekly Second Contact event on Wednesdays. A Tier 5 or higher Cerritos can join Second Contact Elite, a rotating weekly event. A Tier 12 Cerritos that completes it also earns Rare Culver Particles. You need them for elite research nodes that improve Support.