From here on, the goal is a base that keeps working while you're away: the Breaker hits, the Collector collects, the Supplier carries to the Port, and you drop by now and then to sell.
Power First
The Breaker and the Collector run on power. Place a Charcoal Burner (burns charcoal) or a Solar Panel from the Power research: every machine inside the generator's circle runs, no cables. If power runs short, machines slow down but don't stop; a machine outside the circle doesn't run at all.
Breaker + Collector
The basic pair. Put a Breaker in front of a resource and a Collector right behind it: the Breaker hits, the Collector sweeps up what drops. Both are made at the workbench and unlocked by the Logistics and Breaking research. The Breaker's head is the same tier as the stone pickaxe: a vein your pickaxe can't open, it can't open either.
Stand Close and It Comes to You
What a station makes goes straight into your hands if you're standing next to it; if you're far away, it drops to the ground and the Collector behind it picks it up. So for your chain to work, you have to walk away from it — if you stand over it, you collect the output yourself and the Collector sits idle.
Lock the Output
In the panel of the furnace at the head of the chain you can turn on "Leave finished work on the floor". Then ingots drop to the ground even while you're standing next to it, and go to the Collector. It's off by default; turn it on if you're building a long chain.
The Relay Skill
Relay on the Skills screen (K) removes this distance rule: work a station finishes comes to you wherever you are. It sits on the last shelf of the skill tree, so it unlocks after you buy the 7th island.
Supplier → Port
The last link. A Supplier fills the Trading Port the way it would fill a chest: it takes from the chest next to it and drops into the Port's iron-edged dock. A chest you put next to the Port does nothing on its own; only a Supplier moves items. You stop by now and then and press sell. The Supplier is researched at the Monument on the 1st island, the Port at the one on the 2nd.
Further On
The next rungs are at the Monuments of more distant islands: the Vacuum and Spreader, the Soil Miner and Water Pump, the Fuser and steel, Breaker II–V, the Throttle, the Reception Tower, rail transport (Rail Depot, Freight Cart, Powered Rail) and, last of all, the Slag Furnace, Reactor, Foundry and Resonator.
Nothing on the ground has an owner. You can take the ingot that comes out of your friend's furnace, and they can take yours. It doesn't matter who built the chain. The purse, islands and research are shared; skills and the quest book are each player's own.