While there are several ways to stick a mirror to a wall in your home, a more permanent method involves actually gluing the glass to the wall using a special adhesive. While this method can be tricky and somewhat messy if you're not careful, it does avoid the use of unsightly brackets.
Gluing a Mirror to a Wall
Measure the wall to make sure the mirror will fit. Making sure that all of your measurements are accurate helps you decide the precise size of mirror you'll be needing and whether it will fit where you want it to go.
Set up the piece of wood against the wall to serve as a support for the mirror. This will prevent the mirror from moving or sliding while you wait for it to dry. Use this opportunity to put the mirror in place and to see if it is to your liking. Make sure it is level.
Load the the special mirror glue into the caulk gun and apply it to the back of the mirror being careful not to put the glue too close to the edge of the wall-side of the mirror. If you do, the glue will seep out and cause a mess.
Push the mirror tightly against the wall and let it sit for at least 24 hours. Use anything you can to keep the mirror against the wall to prevent it from moving. The piece of wood will provide base support, and you can use a sturdy adhesive tape to help hold it up as well (use on the top corners). You also can lean something against the mirror to help hold it against the wall.
Let the glue dry. After at least one day, you can remove the supports for the mirror.