How do viruses and their removals work?

I am writing a story and a virus is involved
currently. I would like to know how viruses work,
an in-depth explanation. I'm a bit above average
in terms of understanding computers, but
certainly not an expert. I read something about
resident and non-resident viruses. One, does
this mean that the replicating part of a virus is
attached to a file in a resident virus, and two,
does it mean it can only replicate when that file
is opened/executed/whatever? I also have no
idea how a virus is removed, and in this story it
is done without the aid of an antivirus program,
so please fill me in. Thank you in advance.

Computer viruses are nothing but computer code, just like the code that draws the web page you're looking at. The only difference is they are designed to do malicious things to your machine. People that design them look for areas of vulnerability in operating systems, browsers, email clients and other programs. A point of vulnerability is a weakness in design that allows the virus to get executable code into your machine and run it.

A self replicating virus is a file that doesn't do anything malicious, it just checks periodically to make sure the malicious code is running and if not, installs a new copy, most often under a new name. Self replicating mal-ware is much more difficult to remove.

Virus removal is done many different ways depending on the software but most of them identify sequences of code (called "footprints") that are unique to that virus. The user periodically uploads a new file of footprints and the removal program scans the machine looking for those footprints and either disables the file by changing the file name or deletes it.

The makers of operating systems, browsers and email clients have made great progress in dealing with viruses in the past few years to the point that the major vulnerability now are machines that aren't kept up to date or machines running proprietary software with poor designs.