If you are looking for the easiest/fastest way, you can use the month-long flight search feature of the ITA. If you want more accuracy and precision, take a look at the KVS Tool FAQ for keyboard shortcuts that can considerably speed-up availability checks for consecutive dates ...
This is what I see from the FAQ:
Q: Is there a way to request availability across multiple dates? What if I am looking for a specific class (or classes)?
A: Not directly, but you can use the <Ctrl> + <PgDown> keyboard shortcut to quickly check availability for subsequent dates. If you are looking for availability in a specific class (or classes), you may also wish to do this in conjunction with the appropriate [Filter] options.
However, expertflyer apparently (I do not subscribe to it) does allow a simultaneous display of all data (awards, upgrades etc) on the requested date +/- 3 days (ie one week in total). In a future upgrade, do plan to add this feature to the KVS tool? See "flexibile search" feature of expert flyer (link:
http://www.expertflyer.com/rates.jsp).