I need to draw a dialect map, splitting an area up into differently coloured regions. Is there an online tool for creating dialect maps? Of course, any map drawing tool where I can take an existing map and draw lines, shade areas, label etc. would work fine
I don't know of a specific tool for making dialect maps but it does sound like something suitable for OpenStreetMap (OSM) and its many map-making tools.
Egotistically, it would be a great overlay to put on top of another map on my GPS, which uses OSM =) It would make for some silly trips: Are we at the isogloss yet? This is retroflex /l/-country!
There are several tutorials too on Wikipedia on how you can go about modifying them. In particular, the articles titled "Change the colors of a country", "Create and color map zones", and "Cut a map into several sub-areas". The last two of these are in French, but the Google Translated versions of these are quite readable too. Also, read this introduction to cartography with Inkscape.
These articles recommend using the software, Inkscape.