If your relationship allows creation or records via the relationship then you can use a field from the child on a parent layout to create the related record in the child (normally done via a portal in the parent, but it also works for a single related field).
There are also techniques setup like this using a global in the parent relating to the child table, which has some advantages. There are a number of articles in this forum relating to this.
However... I have found that scripted techniques are better because you can control over record commit, layout control, validation etc... there is more "control" when using scripts.
As Peter mentioned, the normal method for doing this is to use a portal. Set the relationship to allow creation of related records. Whenever someone types information into a field in a blank row, FileMaker will automatically insert the parent key value in the child record.
The technique PeterWindle has referred to is sometimes known as Magic Key and there are articles that describe it in more detail: