1) Draw crappy icon in any of the zillion free icon editors out there (e.g. IconEdit32).
2) Name the file 'favicon.ico' and upload it to the root directory of the website.
I have a feeling I should be doing consulting in the UK or something.
If I tell a designer to create the front page of a feature-packed, online store where every tiny decision has a significant impact on sales figures, and the process has to be run past (and work for) countless people within the organisation - no one is doing that in under an hour!
In this case, there's every chance that the actual decision making process was "resize logo or part of logo to fit a small square", but there's also a chance that other options were considered, a couple of meetings were held to get it approved, etc.
Not as easy as it sounds.
I say that because I remember it taking me only a few minutes to go from knowing nothing whatsoever about them to making my own.