You can get mirror brackets/clips intended specifically for this use. Here are two examples:
(of course, you need to get ones in a matching color and texture or color them yourself etc.)
As for placing them, you have multiple options:
- One bracket at the center of each of the four sides of the mirror (top, bottom, left, right)
- Two brackets at 1/5 and 4/5 of the bottom and the top (or even closer to the left and right edges)
- Two brackets at the bottom and the top + two brackets at 1/2 of the left and right sides.
- Some brackets are intended for corners; in that case it's one at each of the four corners.
- etc. etc.
Here's an example of option 2:
