How do you figure out which electrical wire goes to where?

There are specific code requirements for the use of white, gray, green, bare, and sometimes orange conductors. Other colors are a matter of convention and may differ from one area to another and certainly from one country to another.

In the central United States where I live, black, red, blue, and white are used for 110-240v; brown, orange, yellow and gray are used for 277/480v and higher voltages. You may encounter other colors but without knowing what specifically you are dealing with I cannot answer further.