If you define
export DOMAIN_HOME=/path/to/domain in your .bashrc.bashrc in your home directory that is sufficient to define it.
After adding the changes there simply log out and log in again for the changes to take effect.
WhenIf instead you define
export DOMAIN_HOME=$DOMAIN_HOME:/path/to/domain you are effectively saying set domain home equal to what is already there and append ":/path/to/domain":/path/to/domain to the end of it. This is not what you want.
If you just type the first exportexport command in your terminal session this value will be valid for the period of your terminal session, and should be enough to test what you need.
Just remember that unixUNIX is a case sensitive beast, unlike windowsWindows, so entering ExportExport is not the same as entering exportexport.