Do you mean elemental (N,P,K,S,Mg,Ca,Fe,Cu,Mn etc.) analysis of plant extracts? Agricultural scientists estimate plant elemental composition by spectrophotometric, titrimetric, flamephotometric, turbidimetric etc. analyses. Autoanalyzers are also available. Atomic absorption spectroscopy is employed for trace elements. For plant elemental analysis, powdered plant biomass is used. Any standard textbook on plant elemental analysis provides details of analysis.
Or do you mean by proximate analyses such as ash content, moisture content, carbohydrates, proteins etc.?
Not yet mentioned analytical methods for the determination of mineral concentrates are:
1) The Rietveld refinement technique - neutron and x-ray diffraction of powder samples for use in the characterization of crystalline mineral species.
2) The fragments of a mineral concentrate can be embedded in an epoxy resin mold. The preparation is then ground and polished on one side. The polished surface can then be analyzed with or without polarizers in dispersed light or reflected light. This lets you determine the shape, the color, and the internal structures of the mineral species.
3) A polished sample preparation can also be polished on both sides and a thick or thin section may be prepared and analyzed with a polarization microscope.
Let me show in addition to my last answer some pictures of microscopic preparations of mineral mixtures from the processing plant of a lead-zinc silver mine in Bolivia.
Upper picture shows a lead-zinc-silver concentrate embedded in epoxy resin with differences in brightness, color, grain shapes and internal intergrowth.
Middle picture shows mineral fragments embedded in epoxy resin of the tailings, with differences in brightness, color, grain shapes and internal intergrowth.
The bottom two images show a thin sections (20 microns thickness).
Left: Transmitted light, parallel polarizers. Differences in transparency, color, grain shape and pleochroism are clearly visible.
Right: Transmitted light, crossed polarizers. Grain shapes and differences in the interference colors of quartz grains and others are clearly visible.