Plain text as you know has no formatting options. You cannot bold/italic/underline anything – but you can use specific characters to represent formatting that are easy to remember.
The old-school way of emphasis was to type in all caps. All caps is and has been considered TO BE SHOUTING for years, so you can’t do that anymore unless you want to look like an idiot. You can however use "enhanced plain text". This is a standard feature in the Mozilla Thunderbird mail client, but even if not using a mail client which recognizes enhanced plain text, it’s still easy to understand regardless.
For bold, surround with asterisks:
She sells *seashells* by the seashore.
For italic, surround with forward slashes:
The rain in Spain falls /mainly/ on the plain.
For underline, surround with underscores:
I'm a mother pheasant plucker; I pluck mother pheasants. I'm _the most pleasant_ mother pheasant plucker who ever plucked a mother pheasant. Signed, Ophelia Bhutt.
When you feed the need to emphasize text (particularly on SMS), using enhanced text is the way to b/i/u your message.