Accommodation in Edinburgh during August tends to get booked up weeks (or even months) in advance, so you should start looking for a place to stay right away. To get you started on your search try:
If you would like to stay in gay-friendly hotel or guest house try:
If you are looking for self-catering accomodation, particularly for a group of people, try the following agencies:
Another popular option for self-catering sccomodation is university halls of residence (aka dorms for American visitors):
Finally you could always try posting an accomodation wanted ad on either the Fringe website or of course on the gay:ed:fest notice board: