How do you get dry soil from wet soil?

You can keep the soil in the sun and turn it over frequently and eventually (depending on its wetness and the amount) your soil will be dry from evaporation.

For quicker methods for smaller amounts, you could heat it in a very low temperature oven for several hours. This method is commonly used in geotechnical engineering laboratories to find the water content of a soil by measuring it's mass while wet, then again when dry - the difference allows you to calculate how much water it contained. However, depending on what you will use the soil for, this may or may not sterilize or affect the qualities or contents (such as good bacteria, etc.). Too high a temperature can also affect the mineralogy of the soil (it can alter the chemistry of the minerals) and alter the soil structure.

There are some chemical and other product additives that can help large areas stay or become drier. Tilling the soil to turn it over and allowing the sun and wind to dry it is perhaps the best approach for fields, but if too wet, you will only compact the soil into clumps that will take longer to dry, and you and your tiller or tractor could get stuck in the mud.