This site contains a great deal of basic information about simple soil tests. The Soil Quality Test Bucket recommends simple equipment and resources for field tests, including pH and EC probes, nitrate and phosphate test strips, and others, and lists where they can be ordered.
A simple test for estimating proportions of sand, silt, and clay in the soil. Texture is one of the most important properties and affects the soil’s potential water and nutrient supplying potential. It is needed to estimate soil water content by the method below.
This site gives guidelines, including photographs, about how to estimate the amount of water a soil is holding as a proportion of it’s water holding potential, split up by soil textural classes (sandy loam, silt loam, etc.). It is also available as a printable brochure. For rangelands, this method can be useful for comparing where in the landscape and vegetation patterns soil moisture is being held or lost in the hours after a rain.
The Comprehensive Assessment of Soil Health manual from Cornell University describes many soil tests and what they mean in terms of soil health. Reading this requires wearing Wyoming goggles because it is generally written from the perspective of regions with higher precipitation, and therefore higher productivity and soil organic matter contents.