When you start playing, you might not be able to find many Turnips on your game-world, but the longer you play, the more Turnips will spawn. Staying close to suitable Biomes might raise the chances to make Turnips grow.
The "Pro" world option "more regrowth" should let even more Turnips spawn even faster.
Grown Turnips can be used in the Cooking Station to cook a wide range of Soups, Sandwiches and Pie. Food can be consumed by player characters to be granted many different buffs (positive effects) and also fed to Pets so that they can then be harvested from.
Seeds cannot be eaten by player characters or Pets directly.
You can grow Crops like Turnips from Turnip Seeds on tilled blocks of Dirt, green Grass and/or Mud. First place such natural blocks over a body of Water or Mineral Water, or alternatively place these liquids directly adjacent to each block of Dirt, Grass or Mud (like directly below for example, or at least corner to corner).
This can even be done underground in complete darkness and/or in a building, but not at too high altitudes, not in too cold nor too hot Biomes/layers, and not too close to Swamplands or pools of Bog Water. In these cases, Seeds will stay "fallow" and won't grow (they can be picked up again though).
Next craft a Plow and use it on the solid blocks to till them; they will turn into "tilled land". Then place Seeds on the tilled land (just like you'd place any block). You can, but you do not need to fertilize Seeds in order to make your Crops grow faster.
Wait a bit until the Crops are ripe to receive the best harvest. Wheat needs approx. 50 minutes (real-life-time) to grow from seeds into ripe plants, even if you're offline. Lettuce needs about 60 minutes, Turnips not much longer (ca. 61 minutes), Horned Melons need ca. 90 minutes until they're ripe.
Crops can be harvested by being "pulled" with the gauntlet and left mouse button (by default) just like any other type of block, item, plant or liquid. If Crops stay "ripe" for 24 RL hours, they will turn into "grown" Crops. The harvest will become a little less then, but Crops won't wither.