Edit Jan 4, 2013:   2013 Whitney Lottery information is ~~here~~

Edit June 8:   The Unused Whitney Permits numbers can be seen here:  2012 Unused Permits.

Edit April 2:   Check Recreation.gov for remaining permits (A=Avilable, R=all reserved). If someone cancels a permit, it will show up as Available on the start date of the permit returned. Here are the links for the available slots. Click "Update Availability" to see the 2-week display of available permits:
  Mt Whitney Trail Day Use availability         Mt Whitney Trail Overnight availability

Important links from Inyo National Forest:
    Mt. Whitney Trail brochure
    Mt. Whitney Trail information web page
    Permit Pickup Instructions - Mt. Whitney

Edit March 26: The lottery winners have been notified. Any slots left become available April 1.
    For more info see:   The Mt. Whitney Lottery - as of March 26, 2012

Edit March 16: The lottery application period is now closed, and credit card charges are showing up.
    For more info see:   The Mt. Whitney Lottery - as of March 16, 2012

Reservations will be made through http://www.recreation.gov

More information here: http://www.fs.usda.gov/Internet/FSE_DOCUMENTS/stelprdb5342664.docx
                    And here: Mt Whitney Permit Reservations 2012

Brent N's original message:

I'm not seeing a lot of difference between the old and new system in terms of timing. Under the new system, lottery permits will be accepted from February 1 through March 15 and results will be sent out before April 1st. The real changes are that we will submit and receive results electronically, reservations can be changed electronically, and we can only list 10 alternate dates. I had hoped that the new system would bring instantaneous results, but alas, the government is still trying to teach us patience.

The website appears to let you attempt to reserve permits now, but no dates are available and I suspect won't be available for immediate reservations until after the lottery has completed.

Brent N