The crank arm on my bike fell off. How does one re-attach it?
The first two threads on the spindle look stripped, meaning the nut will have stripped threads as well. The square taper in the crank is almost certain damaged from being used while loose. In other words, in my local slang, "it's munted"
The proper, safe and reliable fix probably requires a new BB spindle and almost certainly a replacement crank.
If you do not want to spend that much (I don't recommend this, as the crank coming off is a safety concern), replace the nut - its cheap. If you can source an used crank it should only cost a few dollars (local bike cop, recycle center or rubbish tip) I would do that rather than reuse the one that has fallen off.
As already said, the nut and a washer will be under the dust cover on the crank.
The picture appears to show a cover over the access hole in the crank arm. Remove the cover by either unscrewing it of prying off the crank arm. Inside you should find a flanged nut. Wipe any grease or grit off the shaft Install the crank arm in the correct orientation onto the shaft. Tighten the nut with a socket (usually a 14mm) to between 300 and 400 inch pounds. Reinstall the dust cover.