Test your soil using a kit to determine how much potassium is already there. Adding too much potassium to the soil might prove detrimental to your plants.
Plow or till your soil a full season (three to four months) prior to planting, creating furrows at least 1 foot deep. How much depends on the type of fertilizer and the effect you wish to achieve. You will need between 5 and 10 pounds of wood ash per 100 square feet for a depleted organic garden, or 0.17 to 0.5 pounds of the chemical potassium chloride for the same area.
Till the dirt again to blend the fertilizer deep into the soil. Leave the soil alone for the remainder of the season, and plant your seeds or sprouts when the weather is right. For carrots, that means waiting until the daytime average temperature is in the lower-to-mid 70s Fahrenheit and nightly temperatures are in at least the 50s, which is early spring in most parts of the United States.
Test the soil prior to planting and again at least once during the growing season to determine if the plants need more potassium.
Add more potassium to the soil to continue feeding the plants by using a chemical or organic plant food with high potassium ratings. Many organic and chemical fertilizers rich in potassium can damage the roots of sprouts and small plants, so only use mild fertilizers or plant foods that are labeled as specifically safe for direct application to plants.