One method is to use the data in the selected portal row to perform a find on your layout for that record. That approach switches your layout's current record to that of the record you clickec and then any such "detail" fields will automatically display data from that record.
It's also possible to set up a second relationship based on a link from a global field to this same table. In that case, the script uses set field to copy the Serial Id of the selected portal row's record to this global field and commits the record. You then add your detail fields from this new relationship's table occurrence and they will display data from the selected portal row's record.
In either case, you either add a button to your portal row that performs such a script or select all the fields in the portal row and use Button Setup... to convert them into a button so that clicking anywhere in the row performs this script.
Here's a script for the first option:
Set Variable [$ID ; Value: YOurPortalTO::ID ]
Enter Find Mode  //clear the pause check box
Set Field [Layout'sTO::ID ; $ID ]
Perform Find 
#You can add a Show All Records and a Sort step here if you want to still navigate to other records by clicking controls in the status area