Debian package files?
 

-rw-rw-r-- 1 chris chris 2148 Mar 17 2015 cuda-repo-ubuntu1404_7.0-28_amd64.deb

When I download files that appear as .deb ...

...Do I just treat it as a .zip file or is there anything else I should do?

Chris:

You could look at it graphically with the File Manager on your OS.
"Thunar" in my Xfce (not xubuntu)
Double click same should (may) prompt you with gdebi-* to install it.
Or
You could install it via the c-line using
Reference: https://help.ubuntu.com/community/InstallingSoftware

Ask if you have any further questions!

Mmmhmm. Thanks!

Before I do that, could you give me a brief, practical explanation as to what repositories actually are, and where this cuda repository would be or how I would create it?
Sorry for being an idiot hahaha.

A repository is a source for software on Linux. Kind of like an App Store. Add more repositories, and increase the amount of software you can get. Just know that the more repositories you add, the more time it will take to check for updates/find software.

If I'm confusing you, check here.

I see you're using Ubuntu, so installing .deb files is quite easy. Just double click it. It will open up the Ubuntu Software Center, and you just click the Install button. Done.

Install gdebi, if it's not already present. It will appear in the right-click menu in your file manager when to select a *.deb file.

Installing from the repos rather than from a downloaded *.deb file, though, is preferable. This article is a good intro the the concept and use of repos.

So just go clarify, if I was trying to install cuda from the repositories, I would say something like

and this would just... automatically install the latest version of cuda from the Linux repos?

Yes if the actual package name is cuda. One last piece of advice I'll give you:

Install Synaptic package manager, run it and update the repos, then type what you're looking for in the search box and it will narrow the list presented to stuff that's applicable. Read the descriptions and install what you want...

Thank you! Okay I've finally sorted this sticking point out. A lot of my other problems should be solved now.

p.s. sorry if you thought I was "taking your advice" before- You just needed to be a bit more clear. I was quite confused, but it's all sorted now :)

We were all clear, you just need to apply a bit of effort in understanding the advice you've been provided...