In my word there should be at least as many records in the join as the sum of records in Group and Personal and plus one for every more joins on either side?
Rethinking this: Not sure that's the truth... probably 1 join-record for every join perhaps, so if one Group has 3 Persons there is 3 Join-records and if one other Person belongs to 3 other Groups thats 3 more Join-records ?
This is how it looks:
So, where do I link the 2:nd instances of the of the 2 "tables" under the others?
...and this is how I think the Join-table should look as, as an example.
Your screen shot of your relationships looks correct. But your sample table appears to contain errors. The third Person record shows a PIDx of 3 and this would not link to a Join record with a PIDx of 5. Perhaps that was a typographical error?
A join table record will link exactly one person record to one group record. So for any one person, there will be as many join table records as their are groups to which they are linked and for any one group record there will be as many join table records as there are person records that belong to that group.
I suspect that the problems you are having are due to mistakes in your layout design. The simplest layout design for working with a many to many relationship is to use a portal to the Join table that includes additional fields from the 3rd table. As an example, you can place a portal to your Join table on Your Person Layout and use it to select Groups for the current Person record displayed on your layout. A group name field from the Groups table can be included in the row of the portal. And a simple way to select a group is to format the JGPIDx field as a drop down list of GIDX and Group Name values.
Here's a demo file where this approach is referred to as the "basic setup". It matches contacts to events, but if you were to rename them Persons and Groups, you'd have the same setup you are trying to create here: https://www.dropbox.com/s/oyir7cs0yxmbn6i/ManyToManywDemoWExtras.fp7
I have only describing a single portal for adding people as a way to make sure that your layout design works.
For a "checkbox" approach, there's a version of that in the demo file.