Starting on day 1 of Summer, Year 1, you can take other farmers' fields by Conquest.
Unlocking Conquests
You can do Conquests starting on day 1 of Summer, Year 1. There will be an automatic cutscene when you wake up that day, where Veronica will invite you to a meeting at the Guild. She and Eda will explain Conquests to you, Giorgio, Elise, and Fritz.
Start a Conquest
To start a Conquest, go to the Guild and talk to Veronica about renting a public field. If any farmers' fields have 0 days on the lease, there will be an exclamation mark over that field. You can choose that field to start a Conquest.
Choose Conquest Type
You can choose to have a Conquest based on different types of competition.
If you choose Yearly Event, Veronica will choose a Yearly Event, and the rights to the field will go to whoever wins that event.
If you choose Shipment Earnings, Veronica chooses a day of the year, and the rights to the field will go to whoever earns the most money from selling things in the Trading Depot that day. If you win, the field will be awarded to you the following day.
You can also have a conquest based on Shipment Variety, where the person who ships the widest variety of goods that day will win the field.
Why To Do Conquests
Are conquests worth it? There are two main benefits: crops planted in the public fields grow more quickly than those planted on your farm, and there are crops and goods that you can only get from the public fields. For example, Rice Seedlings will only grow in the Water Paddy, and the only way to make Honey and Mushrooms is to use the Bees and Mushrooms field.
Overall, this means that Conquests can lead to more profit for you.