While one could change the wallpaper even in Windows 3.1, you cannot do so in Windows 7 Starter Edition. Moreover, by default, Windows 7 Home Basic edition allows you to change the desktop wallpaper only by right- clicking an image and clicking Set as desktop background.
There is this free software called Oceanis Change Background Windows 7 that lets you change the wallpaper.
After downloading and installing it, you will have to restart your computer. On restart you will be greeted with a rather amusing cartoon:
While I did install the program, I did not really try it out, but I understand that it also lets you rotate the wallpapers and create a slideshow too. If any of you do decide to try it out on your Starter Edition, please do share your experience here for the benefit of others.
Do note that Oceanis however does need to run as a process in the background in order to keep the wallpaper modified.
Download: Softonic. (De-linked because download link is broken)
You might instead want to check out how you can change wallpaper in Windows 7 Starter Edition easily and Personalization Panel which allows implemention of the premium personalization features to Windows 7 Starter and Home Basic Editions too.