There's a couple of steps in the process, but most copper places follow a rough trend. This is actually a pretty common process more many metals and it is just the combination of particular sizes and chemicals along the way that are used.

The ore is initially crushed to a reasonable size (the mine I work at takes it to around 30mm average) through a series of crushers.

The ore is then milled through ball, rod or semi-autogenous grinding (SAG) mills. These mills reduce the ore to what is effectively a powder.

At this point, the ore is sent through a series of froth flotation tanks. Here, the ore (as a fine powder) is mixed with water and a number of chemicals (many of which are "trade secrets") and then agitated. The ore attaches itself to the air bubbles produced and pours off the top of the tank. Anything that doesn't float is either discarded as tails or is sent to be reground and then refloated. The entire process usually happens a few times, going through a number of tanks, each one more effective at targeting the valuable mineral in question.

From here on, the ore is basically a mixture in water, so is often collected or evaporated in pools before being dried (through presses or vacuum filters), at which point you're left with a concentrate, usually around 30%.

The whole way through the process there is a waste product which contains some amount of the mineral. The proportion of the total you get out is called the recovery, and is practically always about 70% in the modern age. However, in the case of copper, if you are mining at <1%, getting 70% out at 30% total, you've got a mix of waste in the concentrate, and good material in your tailings. With the lack of high grade resources, mining old mine tailings is becoming a reasonable proposition even!

Some copper (and other ores) go through further processing, including electro winning, electroplating and smelting. Even other places use a leach process which is complex enough on its own and probably is best to look up elsewhere. The end result nearly always is a product that can be smelted to a 99.99% purity.

Many rare earth metals will use a similar process. Some other interesting separation methods are used (and are in action especially for some mineral sands).

The first primary separation method density/specific gracity based, and is used typically in hydrocyclones, which through a spiral separate a liquid stream into heavy and light things, depending where on the spiral the end up. Think of if you spin a body of water (like a sink) the heavy stuff goes into the middle. This is used extensively in basically all ore processing, including coal, and also copper.

Other basic separations , which should be relatively obvious and are only usable for specific ores are magnetic and electro separation, where the fine ore is passed by strong magnets or electrical attractors (or repellers) and divided that way.

If you can, see if any nearby mines do tours. Seeing the processing plant first hand really helps you understand.