If you define

 export DOMAIN_HOME=/path/to/domain

in your .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.

When 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" to the end of it. This is not what you want.

If you just type the first export 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 unix is a case sensitive beast, unlike windows, so entering Export is not the same as entering export.