From the Press Release
"The Mac OS X Lion Up-To-Date upgrade is available at no additional charge via the Mac App Store to all customers who purchased a qualifying new Mac system from Apple or an Apple Authorized Reseller on or after June 6, 2011. Users must request their Up-To-Date upgrade within 30 days of purchase of their Mac computer. Customers who purchase a qualifying Mac between June 6, 2011 and the date when Lion is available in the Mac App Store will have 30 days from Lion's official release date to make a request."

Apple has yet to post specific details about the Lion Up-to-Date program thus, consumers will have to wait for further information on how the upgrade will be handled by Apple.  In our view, Apple will have to either clarify or remove the following statement as it implies that users will have to request the upgrade within 30 days even if Apple does not release Lion by July 5, "Users must request their Up-To-Date upgrade within 30 days of purchase of their Mac computer."  In fact, it conflicts with the "30 days from Lion's official release" statement that Apple provides later in the program's description.

We believe the latter will apply, customers that have purchased a new Mac with Snow Leopard installed as the base operating system will have 30 days after Lion is released to request the free upgrade.

Check Apple's Lion Up-To-Date Page
Apple has created a dedicated Lion up-to-date page. which will be updated once an official Lion announcement date has been made, this will occur sometime in July.

Prior programs
In 2009, Apple made a similar offer to new Mac buyers via the Snow Leopard Up-to-Date program - that program offered new Mac buyers an upgrade from Mac OS X Leopard (10.5) to Mac OS X Snow Leopard (10.6) for $9.95, a cost to cover the shipping and handling fee for the Snow Leopard disc.

The Lion up to date program will avoid direct costs to consumers because the software can be downloaded (4GB in size) directly from Apple via the Mac App Store.

You can read Apple's OS X Lion Press Release here.