Metals (including precious metals) are rarely found in pure form in nature. They are usually found as a part of the composition of mineral rocks that have to be processed to isolate the purified form of the metals contained within them. The metal content is often a small overall part of the mineral content, so mineral deposits must be assessed for their potential value.
Basically, the assay value and the grade of an ore are the same thing. They are both an attempt to measure the metal content of an ore sample to determine its value. The assay value measures the metal content as a percentage of the total weight. In other words, the ore might be 4% iron by weight (kilograms). The grade of the ore is the same thing. The term "grade" is more of a financial term. Assay value is simply a more scientific term for the same thing.
As far as determining the assay value of iron (Fe) in an ore, the best way would be to analyze it by an instrument called an ICP-OES (inductively coupled plasma optical emission spectrometer). A sample of the ore is broken down chemically by a process called digestion. This means treatment with a harsh chemical like an acid. The digested sample is put in solution and injected into the instrument. The plasma arc in the spectrometer effectively ionizes and cleanly burns the atoms contained in the sample. Different elements emit unique wavelengths of light. The emission spectrum for iron is scanned for and its intensity is used to determine the amount of iron present. This is usually accomplished by first injecting several standards of known concentration into the spectrometer to create a calibration curve. Where the ore sample falls in the calibration curve will give the iron concentration in the sample. This can be used to back-calculate the iron percentage in the original ore sample.