The first step in making copper wire is what's known as the drawing process. Rods of copper are set on a machine, which will pull the rod through a drawing die. The end where the rod goes in the die is the same size as the rod, but the die narrows, which forces the diameter of the copper rod to shrink and pulls it out to a longer length. This is usually done several times through progressively smaller drawing dies. The drawing process is continued until the original copper rod is the proper gauge to be considered wire. After this first step, it's moved on to the annealing process.
The annealing process is a fairly simple, yet vastly important part of making copper (or any other sort) of wire. In the drawing process the copper was cold worked, meaning no heat was applied to it. Because of all the stress and strain, the copper is fairly brittle after the drawing process, not flexible as copper wire needs to be. The wire is then put into an electric furnace for annealing to bring back that flexibility. The annealing process allows the metal to recrystallize into its original structure, softening it, but still keeping the copper in a solid state.
Technically, once the annealing process is complete, the copper wire is ready to be used. However, there are other processes that are typically undergone first. The wire may be tinned, which is where the wire is coated with a thin layer of tin either by hot-dipping it in melted tin or through the electroplating process. Copper wire may also be braided into ropes before it's sold. Regardless, whenever any other processes are finished, the copper wire is wound onto spools and, from that point onward, it's ready to be used.