How do I go about learning how to write scripts for illustrator?

This has been some good advice. If anyone else has any more ideas please share.

I should note, my initial experience with automating Illustrator did not involve scripting at all. I used Keyboard Maestro, a Mac-only app, to write simple macros that did basic automated tasks in Illustrator (and any other application). As my experience and confidence grew I branched out into scripting and incorported them into the Keyboard Maestro (KM) macros. KM allows me to assign "triggers" to any script, making it easy to encorporate them into a larger workflow.

As someone who started not on a programmer path, Illustrator scripting is how I got into a much broader range of technologies from 9 years ago. My first 'real' job was intense and I had to learn scripting to save my poor arm from the typing needed in daily tasks as a production art person.

Back then, resources were more limited and scripting capabilities were more limited than in later versions of Illustrator. However, the software was seemingly more stable and you used to be able to create scripts that would last a long time before some new Adobe change broke them. Also, as others have pointed out, javascript is the cross-platform easiest-to-learn language the general skills of which can be carried over into web design and other Adobe apps. The thing with "ExtendScript", Adobe's javascript is that it's following a really old version of javascript that doesn't have all the same features as the javascript they use in web design. So back in the day, the difference of ExtendScript and the latest javascript kind they ran in browsers was kind-of small compared to what it is now. Additionally some front-end UI design frameworks started to make their own syntax on top of javascript and even encroached on Adobe's ExtendScript file extension of ".jsx" which to us means an Adobe javascript document but a React.js document for a web designer.

So thing brings me to the next point of the code editor because previously we had Adobe's trusty ESTK (ExtendScript Tool Kit) to rely on, and it had syntax checking for exactly that archaic ES3 style of javascript Adobe uses. But as pointed out by others, this will be going away in some OSs soon and all the rest - eventually. So now we have VSCode editor with an "ESTK" Plugin that is used to sort of replicate the old ESTK in a new code editor. And this new code editor probably has some settings to change the syntax for just .jsx extensions in just certain foldres - but I have been too lazy to investigate. Basically, with new complex stuff there's a new learning curve compared to just using the old ESTK if you are still able to.

I'm going on doing some form of scripting for 10 years, and it took probably 5 years to be proficient. This being said, math-oriented stuff I don't do myself as much as I can and I just ask others for advice to implement a common stackoverflow answer to my needs. The first month or two of learning were especially frustrating because I originally began without watching any javascript videos and trying to create my ideal script for that time by pasting snippets from the forum. Using a Head-First javascript book, I slowly also learned some of the basics to make some rudimentary edits to the online snippets and produced some basic results. While in the short-term this was highly exhillarating, I found that I had authored something doomed to fail. Therefore there came a point when I knew that it was in my best interest to tear my work down and start completely over using my experience. After the first month I discovered the Lynda.com tutorials for javascript and it helped a lot because the videos were short and dealing with a specific subject at a time. All the while I needed to be aware of the Adobe vs modern browser javascript differences.

My advice for beginners in Adobe scripting is to keep watching the web-javascript tutorials but also to go to their local half-price books (if there's some in your country or the equivalent thereof) and also try to locate ancient tutorials for really old browser javascript. Those will still have browser features you can't use, but they will have syntax more similar to the Adobe ExtendScript one. Additionally any google search or stack-overflow search for Adobe ExtendScript will yield applicable results - but early on you should get the sense for what the difference between the javascript versions is. To make work inside VSCode faster, learn JSDoc which will help your VSCode have intellisense and auto-complete your code as you type it. While this is not available in ESTK, you can still have JSDoc comments in your old-style files and ESTK will work normally while VSCode will give the extra benefit of auto-completion, but in all cases the comments will help to document your work.
Then, after mastering basic scripting you can expand into using TypeScript which is a way to super-charge your work by making javascript act more like a back-end object-oriented language and creating CEP extensions which can use browser javascript and Node.js server-side javascript in addition to ExtendScript javascript.

Also, while my work touches on any number of diverse software technologies I am hardly a master of all and find myself relying on others for help, new users who ask better questions and give better answers and also google basic questions that I should already have known!

Good luck and have fun!

The thing to be aware of is that, unless you've already learnt programming, you will be trying to learn two concepts at the same time. The first is programming and the second is applying programming to solve Illustrator problems. So I would start with learning programming basics. My introduction to JavaScript was through a little book titled "Make: Getting Started with p5.js" by Lauren McCarthy. That can be read in a couple of weeks. 

Hi cute, 

① How do I go about learning how to write scripts for illustrator?

read the official guides, watch video tutorials, ask question here, read books, dive in and start messing with it. What's your style of learning other stuff?
② What sources are there for this?

same as above
③ How long does it take to become proficient at this (a guesstimate)?

I'd say 2-3 years you should be ready to write scripts for others. But nothing stops you from practicing like a mad person and be ready in 6 weeks.
④ What advice do you give to a beginner?

practice, practice, practice...

Welcome to the "quest". I've been trying to learn how to script for Illustrator for about 2+ years. This is after 32 years of using Illustrator.

First, have you chosen a scripting language? I chose ExtendScript (Javascript for Adobe products) because it is cross-platform and there seems to be more reference for it. I use this site every day:
https://illustrator-scripting-guide.readthedocs.io/

I started though, by learning the basices of JavaScript by watching several Training Videos on Lynda.com. You may be able to access it for free through your local Library account:
https://www.lynda.com/JavaScript-tutorials/JavaScript-Essential-Training/574716-2.html

But the BEST resource I've found is this forum!! The scripting gurus here are very willing to help a beginner.

It seems daunting at first, but in a few months you'll be amazed at what you've learned. 

To answer 1. and 2.:
The scripts brought by the application itself, for example
Illustrator-Installation/Scripting/Sample Scripts/JavaScript
are in fact some kind of teaching-book.
Take a look at the source, it's well documented.
However the examples are not in any order of complexity.
The short ones give you a good insight how wide spead the themes are.
3. It depends on your time and energy. It feels like I am still a noob.