What sort of geological features would you look for to find this precious resource?
Two types, low volume high concentrations, and vice versa. For high concentrations start with gravity mapping, and check out high Bouguer anomalies. Generally speaking basic and intermediate igneous, and metamorphic terraines are a better bet than sedimentary terrains - though circulating groundwaters and water-rock interaction can produce local copper shows almost anywhere. Regional mapping of surface water and sediment chemistry should highlight the areas worth exploring. Search for oxidized copper minerals like malachite, azurite, brochantite, etc.
In Australia one of the richest copper mining areas was famously discovered by a dog chasing a rabbit into its' hole. The dog owner found malachite in the excavated spoil of the rabbit warren.
On the big industrial scale, (high volume, low grade) look for copper porphyry of Andean type, which should be obvious from general geological mapping.
A crude but novel way of exploring is to dump bits of scrap iron in local streams, then check them out a few weeks/months later to see if iron-copper exchange has occurred.
Copper can be found in exploitable concentrations in a variety of environments, most significantly as Hydrothermal (hot fluid) deposits.
In order of significance, here are the main types of copper deposits:
- Porphyry deposits - account for 50-60% of current world production.
- Sediment-hosted deposits
- Red-bed deposits
- Volcanogenic massive sulphide deposits (VMS)
- Magmatic sulphide deposits
- Sedimentary exhalative (SEDEX)
- Copper skarns
- Vein-style deposits
So in terms of geological features, I would look anywhere where there has been a large amount of intrusive rock and hydrothermal fluid interaction, and focus on Porphyry deposits. These would show as anomalies in geophysical surveys. On a smaller scale, it really depends on the local geology - there is a certain concentration of copper all over the Earth's crust, but concentrations of copper may not always show as obvious features on the surface...
A few ways:
1) Accidentally, as Gorden Stranger and his Australian example.
2) River sediments, sometimes companies will go down a river checking for trace amounts of copper, if there is a change along the way then you know there is copper nearby.
3) Where there are no mines, it's highly likely there's going to be a lot of copper in area's where there has never been mines, for example in the middle of a desert.
4) Large quarries
5) How does copper form, if you can work this out then you can map areas where it might be likely that copper would form and you can drill around a bit
6) Landfalls, often you'll be able to see pieces of copper after large landfalls or when bits of cliff break off.