RENTING PUBLIC FIELDS
If you want to rent a field owned by the guild, you can issue a challenge for the right to the land. These challenges are known as "Conquests", and are judged based on several conditions, such as who can ship the greatest amount or highest value of a certain crop in a single day. If you win the Conquest, you'll gain the right to use that field. You can only issue challenges for fields whose rights have expired.
Each of the guild's fields is best-suited to growing certain types of crops, and some fields allow you to grow crops you can't grow on your own farm. Rentals are for a certain period of time, and once that time has expired, you'll need to compete with the town's other farmers for the rental rights.
CONQUEST RESULTS
You can see the results of a Conquest challenge at the guild once it's finished. If you're the winner of the Conquest, you'll be able to use the field you've gained the rights to the next day. If you don't check the results at the guild, Veronica will pay a visit to your house the next morning to inform you of the outcome.