Growing your jarldom
There are three ways to add another isle to your jarldom, and none of them work the same way.
Exact numbers below (prices, odds, timings) are still being tuned, so this page describes the shape of each option rather than promising exact figures.
Buy onePay for an unclaimed isle at the Harbor Exchange. Fast, but it costs gold up front.
Find oneSend ships out on a Survey. Slower, and not guaranteed, but it can turn up land nobody's paying for yet.
Take oneWin the right fight against another jarl. The only way to grow at someone else's expense.Buying an unclaimed isle
Isles that nobody rules yet, called Free Isles, turn up for sale at the Harbor Exchange over time. They're priced the same way as everything else there: buying one moves its price up a little, and the market never gives anyone a special rate for having more gold.
If you sell an isle back, you only get part of what you paid for it. That's on purpose. It stops jarls from flipping isles back and forth just to make easy gold. Isles you buy early in the game, while you're still in Fosterage, cost less than they will later.
This is the simplest way to grow. It just costs the most gold, up front, right when you probably have the least of it.
Finding one yourself
A Survey sends a Longship or a Knarr out to search for land nobody's claimed. It costs one of your Orders to launch, and it takes real time to come back with an answer. Building more Wayfinders' Isles improves your odds of it paying off.
Some Surveys reach past the Maelstrom or out into the open north sea, looking for isles nobody else has even seen yet. Those trips take longer and cost more to launch, but the isles that turn up out there tend to come cheaper than anything back in the crowded, well-mapped waters.
A Survey is the patient option. It doesn't cost you gold the way buying does, but it isn't guaranteed to turn up anything either.
Taking one by force
The only way to take land that already belongs to another jarl is to beat them in a fight, and specifically to win the Strand, the beach-and-docks front of a battle. Win it, and you seize one of their isles. Win the other two fronts instead, and you get loot and a blockade, but not land.
An isle you capture doesn't arrive ready to use. It comes over Dormant, the same quiet state an isle falls into when its upkeep goes unpaid (see the Economy page), producing nothing until you spend the gold to bring it back online. A captured isle is a promise of future income, not an instant one.
Attacking someone much smaller than you barely pays, and it costs you standing with the Harbor Authority. Attacking someone close to your own size pays the most. The full mechanics of how a battle actually plays out are on the Combat page.