How do the two methods (direct and inderect) of calculating operating
activities differ?

Hello baseball2:

Thanks for the interesting question. 

The short answer to your question is that using the direct method
requires more intimate, detailed information about how a company works
and what its accounting practices are, while the indirect method can
be calculated from the information in a typical balance sheet.

The following site gives a good summary of the differences:

The 'Business Builders' Workshop: - 4.  How to Prepare a Cash Flow Statement
URL: http://oak.cats.ohiou.edu/~jb358097/esp/businessbuilders.htm
Quote: "The direct method of calculating operating activities requires
an in-depth knowledge of the business and its accounting methods. In
this method, any use (outflow) of cash is subtracted and any source
(inflow) of cash is added to compute total net cash from operating
activities.
The indirect method of computing operating activities starts with net
income and adjusts that net income to take into account any changes
during the given period according to the balance sheet."

The following website gives more detailed descriptions, along with examples:

How to Prepare a Cash Flow Statement
DIRECT METHOD OF COMPUTING OPERATING ACTIVITIES
URL: http://www.cogentsolver.com/direct.htm
INDIRECT METHOD OF COMPUTING OPERATING ACTIVITIES 
URL: http://www.cogentsolver.com/method.htm

Search Strategy (on Google):
* "calculating operating activities"
* "operating activities" direct indirect
 
I hope this helps!

websearcher

The extra web-site tips were excellent! Thank you!