The common sources of iron ore that are easily accessible without mining are bog iron and iron sand. Bog iron, as the name suggests, is found in bogs and similar moist environments (e.g., along streams); the deposits of ore are formed by bacteria (which will make new ore, and the bog can be reharvested after a decade or a few decades). Depending on the bog, one might have to dig for the ore, but this involves digging in a soft bog rather than mining in rock. The other easy source, iron sand, is formed by the erosion of iron ore deposits. The iron content in the sand is often low, but the iron grains can be separated from the silica sand by panning or washing.

Bog iron and iron sand were, in many places, used as the main sources of iron ore into quite recent times (the 18th and 19th centuries, depending on where). Old-style collection of the ore by hand is not sufficient to sustain modern industrial iron-making (the labour costs would be far too high), but mechanised collection of iron sand is still used (sand mining).

However, the limiting natural resource for iron-making was often wood, for making charcoal, as the carbon source and energy source for smelting, and energy source for working the iron. Charcoal making could easily take more labour than collecting ore (assuming the use of bog iron or iron sand), and the lack of plentiful wood would stop the development of a major iron industry (and deforestation could bring a large-scale iron industry to an end).

Some discussion about the labour costs of bog iron, iron sand, mining in rock, and charcoal making in https://www.reddit.com/r/AskHistorians/comments/8y6u5g/how_iron_mining_differed_from_bog_iron_harvesting/ (and u/tsayper reports a quite remarkable productivity of bog iron harvesting of "750 kg of bog ore in a day per worker").

If there were iron ore deposits suitable for mining close to a source of wood, mining could be used to obtain ore. If the rock was soft enough to be broken by picks, iron/steel picks could be used (before iron, stone hammers, antler picks, wooden picks, etc., were used). If the rock was too hard to be easily mined by picks, fire was used to break the rock. Firewood was piled against the rock face, and lit. Once the fire had burned down, and the rock face was still hot, water was thrown onto the rock, breaking it as the surface cooled rapidly. Picks and fire were also used for mining of other metals, notably copper, tin, lead, silver, and gold. Fire-setting remained the preferred method of breaking hard rock for mining until blasting with explosives became available.

The advantage of mining large bodies of ore is that there is lots of ore in one place, and while it might take more effort to break the ore and surrounding rock, the labour cost of transport will be lower (assuming that one can smelt the ore near the mine).

Other tools are important or useful for mining, such as wheeled mine-carts, pulleys, and pumps. Bulliet (2016) notes that the earliest known wheeled vehicles are mine-carts from Copper Age copper mines in the Carpathians; ore is heavy, and being able to move the ore in cramped mines makes mine-carts attractive.

All three of these sources of ore (bog iron, iron sand, and mining large bodies of ore) were used in ancient India. Bog iron and mining were used in ancient China and by the Romans. Iron sand was used in Medieval and later China, but it isn't clear when it was first used. Iron sand was not a major source of ore in Europe, seeing little use (if any) until the Industrial Revolution. Bog iron and iron sand continued in use in India and China into modern times, until the end of the traditional iron industries in India and China in the 19th and early 20th centuries.

References:

Bulliet, Richard. The Wheel : Inventions and Reinventions, Columbia University Press, 2016.

The Romans mined extensively, and used techniques very similar to those used well into the 19th century. For instance, a gold-seeking shaft mine in 1849 California was very similar to a shaft mine in Roman Gaul. The set them into mountains, into the desert, into rivers, or anywhere else the experts thought there might be deposits. They had iron tools which were nearly identical to those of the 49ers. You can see some examples here from the Hedemünden legionary fort. For your request of 400 BCE, there is not much evidence (or any) for Roman mining. That would be a time period for late Classical to Hellenistic Greek activity. Most Roman mining data is from the first century BCE and then into the Imperial period. I know nothing about mining in China or India.

Iron was (and still is) quite common, and both the Greeks and Romans had the technological know-how to extract it via mining (they did not need to rely on bog iron, and all the bog iron on the whole earth would not supply the amount of iron a Roman army consumed in a single campaign). In the ancient world, iron deposits were plentiful in Italy, including central Italy. At Noricum, up in the Alps, there was an especially-rich source which was naturally carburized. Spain was also a major source of iron.

Gold was extracted also from the Alps, from alluvial deposits using hydraulic methods, and on a massive scale. Spain was also a gold source, especially in the first century AD, where we find evidence of absolutely gigantic operations using hydraulic opencast mining methods for both alluvial and also hard rock deposits. Hundreds of such sites are now known from NW Spain and Portugal. The eastern deserts of Egypt were also a source of Roman gold-seeking, in simple open-pit shaft mines. At one such site, the name of which is completely escaping me, there is some pretty good evidence of ingot casting on-site. This is interesting, because from shipwrecks we find ingots of iron, lead, copper, and tin, but never gold or silver. Presumably the gold ingots from the Egyptian pit mines would be shipped to the sea, or else back to the Nile overland for transport down to Alexandria and the sea. It's unclear exactly why we don't find them in shipwrecks. Some hypothesize that the Roman state, which controlled the extraction of precious metals from the imperial period onwards, would have gold and silver ingot shipped separately, and under heavy guard. That still does not explain how they prevented those shipments from falling victim to storms. Neptune did not discriminate between gold ingots and lead ingots. In shallow water, the Roman state had the resources to mount an operation to recover the lost ingots, but in the deeps those ingots would have been lost. It could also just be a weird accident of preservation of evidence.

For silver, the major and best source for the Greeks was on the Greek mainland itself, usually in smaller deposits. Famously, the Athenian discovery of a silver mine at Laureion (at the southern end of their territory) enabled that city to propel herself into greatness (by purchasing the materials to construct a powerful fleet of ships). For the Romans, Spain was the site of a veritable "Silver Rush," and the amount of silver extracted, beginning in the first century BCE, from places like San Domingos and Aljustrel is absolutely staggering.

For your specifically, I would recommend the book by Robert Shepherd, Ancient Mining London 1993. This is a basic survey of ancient mining, techniques, technology.

Unfortunately, the other quality academic studies for ancient mining are usually not in English. There are a few good English ones, though.

Domergue, C. (2008). Les mines antiques: la production des m´etaux aux ´epoques grecque et romaine. Paris. [if you read French, this is the place to go]

Hirt, A. M. (2010) Imperial Mines and Quarries in the RomanWorld: Organizational Aspects 27 BC – AD 235. Oxford. [Roman, and late]