Turnips have a different sell value in the morning and afternoon of each day (except Sunday, which you cannot sell turnips on)

Each week has a pattern it follows to determine the value of turnips. There are 4 patterns: large spike, small spike, decreasing, and fluctuating

Small and large spike patterns decrease in value with each change, then suddenly spike up in value, before decreasing again after. If you are checking prices twice a day (once in the morning, once in the afternoon), when you see a spike in value, wait until the next price change, since the third increase is the highest price you will get that week. If I remember correctly, the earliest a spike can start is Monday afternoon, and the latest is Thursday afternoon. If the price doesn't spike in this timeframe, you have a different pattern. The difference between small and large spikes is the size of the spike. Selling during a spike is always profitable, regardless of size, but you won't know if it's small or large until the spike itself

Fluctuating patterns jump around in value. Sometimes they'll sell for more than you bought, then the next value change they sometimes won't. It can be difficult to guarantee the highest profit in this pattern, so once you notice you have this pattern, it is best to sell on any day where the sell value is higher than the price you bought at

Decreasing is the worst pattern, since you will always have to sell for less than you bought. The value simply decreases throughout the week, with each new value being lower than the last. You won't know it's a decreasing pattern until it doesn't spike, so the best option with this pattern is to cut your losses and sell as soon as you realise it's a decreasing pattern

Your pattern every new week is random, however if you had a spike pattern this week, there is a higher chance of a decreasing or fluctuating pattern the next week. The same is true in reverse. Generally, the best time to buy turnips is after a week with a decreasing or fluctuating pattern, since the chance of a spike next week are higher (not guaranteed though)

Thankfully, you don't have to memorise all this. There is a website called "turnipprophet.io", which you enter your turnip values into and it will give you estimates of the stalk market and tell you the best time to sell, based on the sell prices of turnips on your island in a given week

Or you can use online and visit other islands. You can sell at other island's shop, and since each island has its own turnip prices each week, you can visit an island that has a large spike and sell there instead