You have to buy the field that is at your left hand near the entrance to your farm.
It's an empty field that has a sign on the middle that says: You need to buy this field.
You have to buy it from the mayor at the gathering house on the town (left side of the plaza) near the library.
It's sold for 250 i think. Just work some times helping the animal dealers and you will buy it in no time.
After that you will see those plots like in Sandy's Farm in that field.