Of course you should create versions for all resolutions/densities you want you app to work with, but for testing purposes one image will suffice.
Let's say you have image called: bg01.jpg
To show it as a background, you should add to you Layout definition:
android:background="@drawable/bg01"
No extension. If you have two files with the same name and different extensions, the behaviour of your application will be erratic at least. Try and avoid it. Even though your IDE may not spit any errors, and you device will handle it gracefully, other might not. If you absolutely need to have same names, for reference for example, keep them in different directories.
If your project is missing the res/drawable directory, you may either create it or forget it and use drawable-ldpi for example. If you decide to create it and use Eclipse or Zend, don't forget to run Project->Clean...
So lets's say You've added that background and it looks great in portrait view, but gets stretched terribly in landscape view:
Without messing with code and creating very complicated rules to find out what view are you using, just create directory res/drawable-land (from landscape), or res/drawable-land-ldpi and in it add a version of the background created for landscape view (turned by 90 degrees most likely). It has to have the same name as its portrait equivalent.
Directory names work the same for portrait views: drawable-port, drawable-port-ldpi.
The result will be:
Beautiful background taken from: http://tiled-bg.blogspot.co.uk/ a gallery of free tile-able website backgrounds.
