How do geologists locate coal or other ore deposits?
Coal deposits are usually first discovered as outcrops in river banks or by people digging water or sometimes oil wells. Most developed countries have a government geological survey group which drills in various places to get an idea of what might be found. As you'd expect, these exploration holes are fairly few so they don't go just anywhere, they depend on reports from local people and even early explorers who assessed rocks on the surface many years before to drill in reasonably likely spots. All this information is archived. Mapping coal deposits generally involves a systematic program of drilling with a special drill that leaves a core inside it, usually 2 inches in diameter, sometimes 6 inches in diameter where much more detail is wanted. These cores can be tested in a wide variety of ways. To assess the ash content of coal the cores can be X-rayed, high ash areas of the core absorb more X-rays. But more usually the core is broken up into lengths and the ash and other chemical properties are measured in a coal laboratory. To a certain extent iron can be found in a similar way as it is often a sort of sedimentary deposit. The large iron deposits in Western Australia though were spotted by a private pilot who flew over them. I think in that case it was known that they were there, he was the one who realised just how big they were. Metals like copper and gold, and silver, lead and zinc are often found together. Often the deposits are initially located by farmers or rural workers who recognise unusual rocks on the surface. This was the case in Broken Hill, Mount Isa and Mount Morgan in Australia and it seems to have been true of the gold in California back in 1849 or so.
That is too general to answer simply. Coal was formed through millions of years of accumulated dead plant biomass, first as peat, then as lignite coal, then as bituminous coal , then as anthracite coal. You find coal in Carboniferous seams in Appalachia and in China and elsewhere or even later Tertiary coal beds in west North America. Other ores depends on the type. Iron ore deposits are made through millions of years of bacteria that accumulate and concentrates iron. The Mesabi Range of North America is an example. If your are really interested in geology, this is a good site to start. www.ucmp.berkeley.edu/carbonifero.
The question is too general: The first thing you do in looking for any mineral deposit is identify the kind of geological environment that the deposit is likely to occur in - for coal that would be non-marine sediments, for metallic deposits possibly a magmatic province. You would then need to study the rocks carefully, sample the streams and soil to see if there were any chemical or mineral signs of a deposit, and you would also use geophysical tools like gravity and magnetics. Only once all this was done, would you resort to drilling which is very expensive.