Personally, I would recommend using a text editor that still has C++ support, just to make your life a little easier. I would try to find one that will still do things like use different colors for various specifics in your code, keep your indenting set up, etc. I personally use TextPad, but I program with Java. I don't know how great the support is for C++. I'm sure someone here who actually codes with C++ regularly could tell you what the best editor to use is.
But yes, you have the right idea. You will write your code in a text editor of your choice, then from the command line compile and run your code. I don't know what command you would have to use to compile or run your code, but I'm sure if you look on the site for the compiler or some of the documentation that may have come with it, it will tell you how.
Edit: Steps 5 and 6 on
this page tell you how to compile and run programs with the MinGW compiler.