If you're using a drop down, are you using a value list tied to the pk of the child table? Could you explain what you are doing in a little more detail? Usually you are trying to populate a child's fk with the parent's pk for a relationship (related record)
If the first field is a number field, auto-complete doesn't work and this is a very irritating limitation of FileMaker value lists. You can't auto-complete on the second field.
I've worked out several ways around this limitation in order to produce the desired result. The simplest actually uses a text field with an auto-complete value list of just the names, but with a look up system supported by scripting to link the records correctly by ID and to also handle cases where duplicate names occur in the table that supplies these values to the value list.
You can find a working example of this in "Adventures in FileMaking - Enhanced Value Selection".
The examples found in this file come with detailed descriptions of how they were set up and how they work.
What is the problem> The Id not populating? Or the Auto complete not working?
If you use a dropdown and the first field is an Id Number field and the second field is a text field then you can type ahead and find the first item with the letter you typed.
That is standard behavior.
Type ahead is not nearly as user friendly an experience as auto-complete.