How are the world's biggest telescopes, (such as the Very Large Telescope for example) cleaned?
One of the ways they clean telescopes is to replace the metal coating on their surface. See, for telescopes, unlike bathroom mirrors, the metal is on the front of the glass. The reason for this difference is that having glass on the front makes the mirror more durable, but it also reduces the mirror's efficiency at creating an image. Because of this every few years the mirror needs to be taken off of the telescope, the old metal removed from the glass by an acid or some other chemical means, and then a new coating of metal is applied. On the tour of the Palomar Observatory they'll tell you that the 5.1 meter Hale telescope uses about the same amount of aluminum to cover it as is in a quarter (not sure if they meant volume or mass - also not completely sure it wasn't a nickle, or 2 quarters).
In the case of telescopes with segmented mirrors, like Keck, they can do this one segment at a time, which makes the process more convenient and spreads it out over time. It's also possible, though I don't know if they do this, to keep segments in backup to put in place of removed segments, because the telescope is made from a relatively small number of segments that have the same curvature and are, therefore, interchangeable.