How do I start getting weekly iTunes U report?

If you are referring to your Private iTunes U site not converted to the iTunes U Public Site Manager, then weekly reports are emailed to the site Administrator email address. Public iTunes U sites I beleive are all using the iTunes U Public Site Manager and weekly reports ceased some time ago but now there is access to usage reports from within the iTunes U Public Site Manager or you can use the iTunes Store API to request Daily iTunes U Log Reports as documented in an updated iTunes U Administration Guide.

I found the API challenging and convinced a collegue to develop a very basic command line app' Laurus to do the hard bit for me. I then import the downloaded data into a database and then do some SQL to replicate the Apple reports.The Laurus app' is not documented at all but if you are interested in using it I should be able to give you some instructions via email or the like.