Welcome to the measuring world!
I use MapMyRun to map the course. I then take various screen-shots: the entire course (map background) to get the overall size of the course onto the page; then zoom-in on sections of the course, and size them to fit over the overall image. Two layers at this point - main overview, and one with the zoom shots.
I use Illustrator, but you can use OpenOffice.org. Both layer. Illustrator is around $400, OpenOffice is free. Illustrator draws better curves, but that is about the main difference.
When you make your maps, put different elements on different layers. As said, overview and zoom shots on two layers. Then, your roads that you draw go on another layer. Road labels on another layer. Descriptive text on another layer. Course lines on another layer. Mile marks on another layer. This actually makes it easier to edit the different elements.
You can be as basic, or as elaborate, as you want. I tell mappers to keep in mind that the map should be made for runners and people not familiar with the area, not just the race director. Clarity, and not cluttered.
Good luck!