Creating my own module and following this guide
http://www.dotnetnuke.com/Resources/Blogs/EntryId/2632/Using-and-Customizing-a-C-Module-Development-Template.aspx
Using this template
http://christoctemplate.codeplex.com/

But after setting everything up and attempting an install on the project to test it, I got this error:
File specified in the dnn could not be found in the zip file: - C:\inetpub\wwwroot\dnntester\Install\Temp\qywivscw\bin\Module_Name.dll

Any idea what that's about? Did I miss or skip some step?

With no access to module I can't say where culprit exactly is, but there are just few options so I'll list them all. Manifest tells installer to get file "Module_Name.dll" from inside folder "bin" which have to reside within said installation zip, but it can't find it. So you either

1. Have "Module_Name.dll" inside root of the zip instead of "bin" folder or maybe not at all.
2. File is named differently, in which case you need to fix it in manifest file (one with .dnn extension)