Players on Windows XP will need to follow the following instructions for playing Don't Starve on fullscreen.
Navigate to your documents folder at Documents\Klei\DoNotStarve\settings.ini (this is default; if you installed Don't Starve somewhere else, you will need to change to that directory)
In settings.ini set the following options:
fullscreen_width = 1280
fullscreen_height = 1024
display_id = 0
refresh _rate = 60
fullscreen = true
Please note that you may need to change the height and width to match your desktop resolution you have currently set on your PC.