I've tried portals but they only display and do not allow entry.
This should not be the case. A portal to a related table is by far the most frequent method used for this scenario. If you open the Invoices Starter solution that comes with FileMaker 13, you'll see an example of a portal being used in exactly this way.
If the portal does not allow data entry, something is not correctly set up either your relationships or your layout.
I've tried a list layout that displays the master info at the top (after entering on a different screen) and it allows me to enter multiple detail records but when I want to start with a new master I can't get it to clear the screen.
This is also possible though it takes scripting to make it work. A script that creates the new master record can then set up a found set of just one new empty detail record. A portal is much simpler so I wouldn't use this approach unless there was a specific need that can't be met with the portal format.
Go to the Edit Relationship dialog box for the relationship between parent and child tables. Make certain the "Allow creation of record in this table via this relationship" is checked. If it's not checked, the portal will not allow records to be created.
If it's not checked, the portal will not allow records to be created.
Many developers prefer not to enable "allow creation" and choose instead to add a button that performs a script to create a new portal record...
Thanks - I think that solves it for me!