$$_Current_Project_ID is a global variable, probably set with a OnRecordLoad trigger. You can go to a layout based upon the child table, create a new record and set its foreign key to that variable and it will become a child of the record you were looking at in the Projects table.
You can find an example attached.
(I prefer passing the parent ID as a parameter to a script, though)
ParentChild.fmp12.zip 68.3 K