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.
Stories must be submitted as plain text* via our web form. Please don't put your address, word count, title, name or other information in the form. Please don't retype your entire story--copy and paste it into the form (once you've saved your document as plain text). If a story is accepted for publication, we'll contact you to incorporate any formatting and layout needed.
*Plain text means no smart quotes, no curvy apostrophes, no magic ellipses, no clever Microsoft formatting that sometimes makes your story harder to read.
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.
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.
The Markdown language was created in 2004 by John Gruber with substantial contributions from Aaron Swartz, with the goal of allowing people “to write using an easy-to-read, easy-to-write plain text format, then convert it to structurally valid XHTML (or HTML)”
MarkDown is the very formatting you will use in posting on StackOverflow/StackExchange.
As you can see from the Wikipedia page, it is very comprehensible even when viewed as plain text. That is the reason why it was invented.
You could then run it over a MarkDown viewer/editor, aka Wiki editor. Software-wise, such editors are comparatively very easy to write, compared to other kinds of formatted word-processors.
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.