After configuring an attached domain for your webspace you can use the 1-click function to install software on the attached domain. Choose the webspace in your control panel and click the 1-click installer menu item. When you are on the 1-click installation page you can choose the attached domain, from the "URL" drop down menu, as the domain you wish to install to.
Make sure not to choose the same table prefix your webspace is using, if you are installing the same system, since this will overwrite the existing tables with the same name/prefix. If you leave the prefix field empty, the installer will create a unique prefix.
Article from the support category: 1-Click installation