I have a mirror but no idea of how to hang it. It weighs about 30 pounds, and is a little under 6 feet tall. Does anyone have any ideas?
Get a nice looking board (maybe 2-3" wide) and the same length as the mirror. Cut a rabbit along one edge (or get a buddy into woodworking to do it if you don't have the tools). Finish anyway you want: Clear, Stain, Paint, etc.) and screw it to studs. Get some mirror clips handy. Set the mirror in the rabbit and install the mirror clips on the top. It may take two ppl: one to hold the mirror in place and the other to install the clips. While it would be best to screw the clips into studs, there will be little force on them so drywall anchors should be fine.
Edit based on comment from OP. Attached is a pic of a rabbit cut. You simply place the rabbitted side toward the wall, making a very sturdy groove for the mirror to set in. Then on the top of the mirror, use mirror or glass clips to hold it in place.
If you got heavy duty mirror clips and found studs in a good location, you could use the heavy duty clips for the bottom of the mirror instead of a rabbited board. But I'm a belt & suspenders kinda guy and like making things strong (overbuilt, my wife says!).
A mirror this large needs more support than just gluing to the wall.
A combination of a bottom metal channel (either a J-channel or an L-channel) is cut to the length of the mirror bottom. The channel is drilled and screwed or nailed to the wall (should be into studs rather than just drywall). This is similar to the piece of wood at the bottom as suggested in another answer but is way less noticeable. The mirror is set onto the lip created by the channel which supports the weight of the mirror. Use blobs of Mirror Mastic (available at hardware stores in caulking tubes) to hold the mirror in place. I would use the same blob spots as you see on the back of your mirror already. Use blue painters tape to hold the mirror against the wall (or mirror clips as suggested in another answer here) for a couple days while the mirror mastic dries.
This is a generic picture of the channel (from an online search for mirror L-channel).
Make sure you use a "Mirror Mastic" rather than any other type of glue. Other glues can damage the mirror silvering on the backside of the mirror.
You can glue it, same as it was before.
All the force is downward, so unless anyone levers it away hard from the wall, then it will stay there.
You need a flexible glue, which will prevent damage due to any movement or gentle knocks, & also be safer if it ever does get smashed, as the whole lot won't come down in big shards.
This is one from the UK - Evo-Stik Light grey Mirror Adhesive
though I think their description went awry at the end. Adhesive doesn't usually have much leather or a mid-sole ;)
This is what they use in shops, gyms, bars, night clubs, etc. where there is real risk of damage.
Read the instructions carefully.