Many people use dedicated map making software, like the mentioned Campaign Cartographer and Fractal Mapper. The truth is that most here create their maps using GIMP or Photoshop which are full featured graphic arts software rather than making just maps. I use Xara Xtreme (Xara Designer Pro is the most current) which is a vector drawing program like Illustrator, Inkscape or Coreldraw.

Really depending on what you want your map to look like - most graphics software have some kind of learning curve. There really is no such thing as software that will let you create a map in one day, unless, like me you're skilled at using the software and can create a world map quickly. There are some stamp applications that are fairly easy to use, but unless you have the right map objects, either it won't look too professional or make only the simplist of designs.

You need to explore the Finished Maps Gallery and look for the kind of map you want. From there you can learn what software was used to design...

There really is no 'push a button' and now you have a nice map - it all takes work, and in some cases training (even if self-training) to do something serious. Map making is art. Art is not a push button proposition, it takes work to do anything.