While there are several ways to make a distinction, you wouldn't always make one in Norwegian. We don't have a continuous tense as you do in English, and though we have ways of expressing continuity we often don't feel the need to explicitly do so.
Depending on what you're wishing to express, the present participle, døende, may be used here. However, it's not something that is going to work with all verbs, or in all settings, so please use it sparingly.
"Everyone here is dying." (imagine a terminal ward at a hospital.)
"Alle her er døende."
"Everyone here is about to die." (/in the process of dying)
"Alle her holder på å dø."
"Everyone here is on the brink of death."
"Alle her er på dødens rand." (/randen av døden)
"Help! I am dying!"
"Hjelp! Jeg dør!" ("Jeg er døende" does not have that sense of immediacy.)