This is a good unofficial website that shows what campsites are available:
http://www.yosemitesites.com/camping/re ... Yosemite/9
June is gone, but late July and early August will open up on March 15th. The rule is 5 months ahead and the dates open up on the 15th of the month. For example, reservations for July 15 - August 14th become available on March 15th.
http://www.nps.gov/yose/planyourvisit/camping.htm
Your alternative is Camp 4, but there's few sites there. You can also reserve campsites outside the valley, but still in the park, in Hodgdon Meadow and Bridalveil Creek.
Crane Flats has 50% non-reserved campgrounds. All campgrounds at Bridalveil Creek are non-reserved, but it may not be open in early June.