There are many ways to draw a scaled map on paper. All of them involve "copying another map" in some way or other unless you actually go out and collect the data yourself as Redrobes suggested. Even if you start from a list of lat/lon coordinates, somebody already had to make that map.

The most important part of mapmaking is knowing why you're making the map. If you want to show local shopping areas then you'll have quite a different map than one showing historically significant activities in the area. Similarly, a modern atlas map of an area will look quite different than a historical exploration map of the area, even though the will try to show the same sorts of things (well, the road networks will likely be a little different, but you get the idea).

Once you know why you want to draw the map (its purpose), you'll be able to decide what media to use, what to include, and what to exclude. The map's purpose will also suggest what type of decoration and annotations the map needs. An antique-style map will likely have a lot of decoration; a modern mapping style will tend to be much simpler.

Once you know what you want to include, then you'll need to choose the visual layout of the map. Is it tall and thin, short and wide, or square? What projection is appropriate? Should it be full-color, a few colors, or black and white? Is it drawn in ink, electronic, paint, or blood?

Now that you know why you're doing the map, how you're doing the map, and what it's going to look like, then it's just a matter of doing it. If you have an example map in the desired projection, a pantograph, photocopier, or projector will allow you to resize the image and place it in the desired place on the page. Then you can trace it in preparation for the final artwork. If you don't have an example map, there are any number of products such as QuantumGIS or Generic Mapping Tools that can take existing world data and let you pick out just the parts you want and project it how you want before producing your cartoon for drawing.

Once you have your sketch, fill in the rest of the details that you decided on and then you'll have your map.