Have the mirror cut to size by a local glazier and adhere to the wall with a type of adhesive called mirror mastic. Mirror mastic is available at local hardware stores and is applied with a caulking gun.
Here are a couple of other unexpected places to stick a mirror, with great results.
Here's a great IKEA hack, using the Expedit shelving unit we all know and love. Design*Sponge shared this picture of a room divider in designer Andreas Uebele's son's room, delineating sleep and play spaces. Adding a mirror to the edge is an instant upgrade.
I strongly suspect this Australian penthouse, seen on Architizer, was not a DIY project, but the idea is transferable to humbler homes. This kitchen island, outfitted with a mirrored base, is endlessly glam. If you don't have an island, you could add mirrors to cabinet faces, or your backsplash.
(Images: as linked above)