Work has asked me to modify/update their website. Where do I start?

I know basic HTML, and made simple websites circa 2000 or so.   Frames were a new thing back then...

I've made brochures & done photography for them when needed.  Fluent in Photoshop.  Things have been slow & I asked if they had need for anything like that, they asked if I could modify/update the website.  I said if I could figure out at least the language/program used to create it I probably could.

I have not kept up on website creation, and have no idea what the current flavors are.  Our website is UPA for reference.  I know some of you out there can help, if you can help me make a grilled cheese sandwich someone can steer me to a program for a website.

Well you're lightyears behind on web technologies so hopefully not too much coding will be involved.

After examining the website I can't find any signs that it's running any popular CMS in the background, it might be using a custom CMS or it could be static pages served through PHP (the most likely scenario considering how tidy the code is and that I see things that have been disabled by commenting them out). If it's the latter, you'll basically have to look through the site code for the relevant content HTML and edit it with a text editor - ideally something programming-oriented like Notepad++ or SciTE.

Edit: I figured out that the website uses the Bootstrap framework at least:

https://getbootstrap.com/

The easy button these days would most likely be a WordPress site with an appropriate theme. 

They aren't asking to redo the site, or even major work.  Just some changing of photos, maybe some different wording here and there.

If I can decide what program would let me open the site/individual pages and edit them, I would be fine.  Did a little Google-fu and see some free stuff and 1-2 paid programs that get good reviews.  I just want to be able to open the site in something and not break anything in the background, and be able to edit and upload either FTP or the File Manager on the host.

Any ol' plaintext editor can edit PHP/HTML files (and just about any other file you're likely to find on a website, apart from photo/audio/video files). Windows' Notepad can do the job (even if it has Unix line endings now!) but a programming-oriented text editor would make things much easier with syntax highlighting, automatic tabbing etc.

A WYSIWYG HTML editor will only do what you want with plain HTML files. There's an old one called Kompozer that works well for that.

Notepad++ helps to make sure that you don't drop a tag and will let you edit text and images the old school way.

Filezilla to upload.

That's about as basic (and free) as you can get.

If you want everything to be pretty, Atom.io with the BeautifyHTML extension helps clean up the code in case you need to break it open again plus it helps to keep the tags and code blocks well defined.

Also, just an FYI, you may also want to edit either your web.config or your .htaccess file to force HTTPS to help with SEO. You can get a free cert from LetsEncrypt.org. Setup is pretty minor.

Looking at more Google I realized my Adobe CS2 has an old copy of GoLive I could at least try exploring the site.  But I think I'd like to download the whole thing to my local hard drive, but the File Manager won't let me.

More Google showed Webcopy might, but it barely downloaded even part of it.  Ugh.  Maybe I don't want this after all.

Are you going to do any analytics ( or is that done as a matter of course in your operation?) on what you have before you launch in to a redesign?

Once you get access to the host's file system you should be able to download the whole site, I use WinSCP for this at work. Getting the site to run on your computer is another matter, you'll have to set up a WAMP stack (don't know if you'll need the database part, if so, you'll also have to do a database dump and then load it into your local server). Here's an easy way to do it:

http://www.wampserver.com/en/

In reply to NOHOME :

There's no redesign.  They simply want me to edit a few pages to change photos, change verbiage for a newer version of an Xray we are now going to sell.  Probably edit other pages along the way.