On sunday mornings from 5am until 12 noon an npc called daisy mae will be somewhere in your town. She will sell you turnips
Turnips come in stacks of 10, and they will cost between 90-110 bells per stack (the price will change each sunday)
Throughout the following week you can check turnip prices at nooks cranny - you will get two different prices per day (one in the morning, and a different price in the afternoon)
If you do not sell them by the following Sunday, or you time travel, they will rot and you'll have to sell them for a loss.
There are some websites online which estimate your turnip prices and help you figure out when the best time to sell your turnips is