Some short story markets (e.g. Daily Science Fiction) request manuscripts in plain text. How do you indicate emphasis in a plain text manuscript?
There is no universal answer to this, as there are many ways of indicating emphasis in plain text. Your best bet is to read the submission guidelines of the publication that you're submitting to, as each may have different requirements.
In the case of Daily Science Fiction, they have a page of story formatting guidelines. As far as I can tell, they don't want any formatting at all.
I would personally find this somewhat strange, but defying submission guidelines is a certain means to have your story rejected out of hand. If I were submitting to this magazine, I'd look for a way to get clarification on this.
However, in general: Read the submission guidelines. Every publication may have slightly different ones.
Either underscores or asterisks around the words, I would think. All-caps run the risk of being printed in all-caps.
In a modern wiki-age, we should use the MarkDown convention, in our plain text scripts if our scripts require textual emphasis or augmentation that plain text would otherwise be incapable of expressing.
MarkDown is the very formatting you will use in posting on StackOverflow/StackExchange.
Experienced wiki authors do not even need a wiki-editor and could write MarkDown in plain text and texted over a phone or to their blog. Just like an aged and effectively deaf Beethoven who could still write phenomenal movements as he was able to "picture" the sounds of his arrangements.
Get used to it and you will find it a very convenient skill. It's not even a "skill". It does not require much skill to read or write it - the reason why it was invented.
In fact, I think Congress (of the United States) should have a bill to have all plain text documents requiring formatting be henceforth written in MarkDown.