In my Cartography Tutorials, I will to show a few techniques for creating maps digitally. First I will say a few words on the tools I used.
For line drawings - for basic outlines of continents, rivers, mountains etc - I use Inkscape. Inkscape is a vector-based graphics program, meaning that if you want to change the map scale later on or move minor details around, you can do so easily without lots of minor editing to prevent weird image artifacts. I also use Inkscape to place the location of cities and similar small details - this allows them to be moved around easily.
Both of these programs are Open Source and freely available for a number of platforms, so you can repeat all of those steps by yourself.
Another tool, while not strictly speaking neccessary, is still something I highly recommend: A graphic tablet. These handy little devices will make drawing lines a lot faster. I recommend a Wacom tablet because they have pressure sensitivity (though you won't need it for what follows, that's still a nifty feature) and because they are simply the best on the market.
Continue to Basic Outlines.