Take a look at Inkscape. It's an open source vector-drawing program. It should feel similar to drawing in Word, but it has a lot more capabilities. For most users, it's functionally equivalent to Adobe Illustrator.
Draw Freely. | Inkscape
Hi. I am trying to find software that would work for my purposes. Right now I want to produce a thematic map of a state. I need to be able to create polygon shapes and points, cut them or combine them, color them, and maybe tag them. I originally was able to make a map on a Word document. While I was able to create shapes (polygons) for counties and color them or make patterns, I could not cut them if I wanted to refine an area. To create a county I needed to retrace all common boundaries, and again for townships. I could also create points for towns, but it rather crude. It was turning into a daunting and clumsy task (especially with boundaries following natural features). I recently purchased a hobbyists mapping license, unaware of its complexity and need to take classes. Does anyone have a suggestion or two? (Feel free to ask questions about what I'm trying to do. I have a Dell desktop with Windows 7.)