I've tried reading other peoples' questions, but I can't seem to modify the
examples to fit my needs.

I have each month's commission payments from our clients on a seperate
worksheet (named January, February, March etc.) which is in another workbook
which may or may not be open. It's probably also worth noting that several of
the sheets are currently blank.

I want to be able create something similar to:

=SUMIF('[Workbook.xls]January:December'!B:B,"Client ID
number",'[Workbook.xls]January:December'!E:E)

where column B of each sheet contains each client's ID number & column E
shows how much they've paid.

Once I've managed this, I need to average the result over the number of
months completed so far (and hopefully have the formula update its result as
new data is entered in my source workbook.)

This feels like a big ask, but if anyone can help it would be greatly
appreciated.