Your Township is given 6 fields when you start. As you level up you can build community buildings which increase your Town's population cap. You can build houses to bring more townspeople into your town. You can earn free fields from the shops Farming section once your population reaches the required amount.
There's a maximum amount of 115 fields since Township v4.4.2.
You can see the amount of fields you have in the Town Hall under the achievement 'Endless Fields' .