Public service announcement: the browser console is strictly more expressive than everything in the page.
Here's (roughly) how:
Open the console
Ctrl-Shift-I in Chrome; I believe Ctrl+Shift+K in Firefox.
Pick out the thing(s) you want
You can pick things out using any of the following functions:
Document.getElementsByClassName(), Document.getElementsByTagName(), Document.querySelector(), Document.getElementById()
(1) This will return a HTMLCollection, not an array, so if you want to iterate over everything you'll need to turn it into an array with Array.from()
(2) If you can't get the exact thing you want, get something that contains it, then use .childNodes to get an array of its child nodes. You can also use all the .get functions on elements to get their children.
Get the details you want
When you've navigated to the right element, use .innerHTML, .innerText, or .value to get the thing inside it. One of them will work, probably innerHTML. value is for inputs.
Do other things on the page
Remember, it's your page, you can do what you want. You can change the .style, you can .remove() things, you can even .click() on things.
It's even pretty straightforward to save stuff to your computer.