When I save AVG to my jumpdrive and when I try to open it on another computer and use it, it does not work. What should I do?

I don't think this will work because AVG needs to be "installed" on the computer. Just copying the files to another drive does not accomplish this. When a program is installed, files are probably written to the \windows directory (and probably others), as well as changes to the registry.

What you want is a Portable App which are specially written programs that do not need to write to the registry and can be executed from a jump drive. A quick look did not reveal an anti-virus app, and this may be because anti-virus programs need a tight integration with the operating system.

I hope this is helpful,
WallyH