How to take screenshots and set a wallpaper
In Qubes OS, dom0 is strongly isolated from the outside world. It has no direct internet connection (for updates, a dedicated UpdateProxy is used to avoid interacting with untrusted data) and copying files into it is highly discouraged and not supported by tools such as qvm-copy.
dom0 is also where the desktop environment and Qubes OS GUI tools are running (unless you are using the experimental sys-gui). Thus, if you take a screenshot or want to set a wallpaper, you will be acting within dom0.
Taking screenshots
In default Qubes OS installation, you can use the default XFCE screenshot tool (called Screenshot), either running it from the Qubes OS menu or using the PrintScreen key.
The file will be saved in dom0, so you need to copy it out of dom0 if you want to use it in any other qube. The easiest way to do it is with the qvm-copy-to-vm tool in dom0 terminal:
$ qvm-copy-to-vm qube-name Pictures/screenshot_name.jpg
Copying files out of dom0 is generally safe for your system.
Setting a wallpaper
As mentioned, all desktop environment tools run in dom0, and copying files into dom0 is a big security risk and strongly discouraged. New users often ask: fine, dom0 needs to be isolated, but how do I then set my own wallpaper in Qubes OS then? The possible solutions are:
copy a file into dom0 in a hacky way (not recommended: this breaks isolation of dom0 and exposes you to risks from a contaminated graphics file)
- use screenshots:
 first, display an image you want in full screen (you can force full screen by right-clicking on the window title bar, see How to enter fullscreen mode for more information)
take a screenshot (as above, take a screenshot)
use this image as your wallpaper
To set a wallpaper in the default XFCE desktop environment, you can use the Desktop tool.
Setting an image as wallpaper within a normal qube does not influence dom0 wallpaper (the one you actually see on the screen) in any way.