What needs to be done in order for a human to be infected by a Red Court vampire? Everything I've seen on this point is pretty vague for some reason.
We Don't Know
The entire Dresden Files series is rather vague on this point. Certain events within the series also make it unlikely to come up. Each of the Vampire Courts seemingly represents some subset of the modern interpretations of vampires. The existence of the more traditional Black Court and the hereditary White Court, as well as the use of the term "Infected", suggests that the transformation may be viral. However, the official answer from Our World is
whether this is by a massive overdose of narcotic venom, a different sort of venom, or something else is unknown
From what I remember in the books, it takes being bitten with the vampire's Will to turn them is the only evidence I've seen beyond "John goes missing, Infected John is here in the next scene". Given the rather quick turnaround in Grave Peril I would say that the actual process takes as little time as the siring vampire desires, but they must be present at the actual turn because it's Dresdenverse magic. There is evidence (implied by changes) that a Practitioner might be able to use thaumaturgy to do it from afar since the transformation is less chemical than spiritual.