They say that the population of Edinburgh doubles during the Festival, which starts with the Festival Fringe in early August, followed by the International Festival, with the Military Tattoo running throughout.
We were there for the Fringe, and it was a madhouse. Depending on your outlook that can be positive or negative. Part of the Royal Mile is closed to automobiles to allow the crowds to roam freely amongst street performers. Just about anybody who wants to can just show up and perform, meaning there is plenty of free entertainment.
It's not all disorganized chaos, however. There are several thousand plays and other shows that are scheduled and require a ticket. The basic idea behind the Fringe is to give performers of all types, with any level of experience a venue to perform, and to be reasonably priced and accessible to the community. Therefore the ticket prices may be only a few pounds, but the quality is hit and miss. There's quite a bit that's good, but a lot that's bad as well. The nature of the Fringe means that you're taking much more risk with your ticket purchase than you might be if you attended a show at the much more conservative (and expensive) Edinburgh International Festival.
The venues used at the fringe are not the posh concert halls and theaters you might be used to either. We saw an adaptation of the Hitchcock film Rope, which was staged inside the abandoned bowels of a building (appropriately called The Underbelly). The show was surprisingly good. The sounds coming in from the street added a sense of realism, while the dark and dank surroundings helped make the subject matter more chilling.
Another show we saw was a performance by a popular comedian by the name of Danny Bhoy. The venue for this show was a festival tent.
We enjoyed both of these shows, but if alternative theatre and unusual venues are not your thing, you may wish to wait for the International Festival.