
I got this advice in 1998. I have the book. I found it useful for the "art" part. It got me through the projects that I was working on at the time, but personally it didn't help me with the fundamentals. Paraphrasing what has been said on this site many times in the past: AoE is a great first book in practical electronics if you already have an undergraduate degree in physics. I showed my brother AoE when he was building guitar pedals and he couldn't make sense of it and said it was obviously assuming things that he didn't know (he had no high-school science background).
There are a lot of potential and/or assumed pre-requistites even for basic electronics: high school physics, first-year calculus, maybe a differential equations course, certainly familiarity with complex numbers. As I understand it EEs take vector calculus and classical electromagnetism, that's a long road for self-study. For that reason it's hard to give general advice about where to begin.
For someone starting out I think the first things to study are DC and then AC analysis of passive circuits (networks of resistors, capacitors, inductors), starting with networks of resistors. Ohms Law, what current and voltage actually mean, some basic introduction to the physics passive components. This is the basics, and I don't see AoE getting anyone over this hump. This could be learnt in many ways, electronics technicians and amateur radio people know this stuff -- there are no doubt courses outside university both on line and in person. If we're talking books, get a second hand copy of Grob's "Basic Electronics." Once that's covered you can move on to semiconductors. I can recommend Malvino's "Electronic Principles," but this book won't teach you about resistors, capacitors and inductors. After that I think the Art of Electronics would be approachable. And also more specialised topics like digital design or operational amplifier circuits.
A book that usually gets a mention is Paul Scherz "Practical Electronics for Inventors." I got that book later, I personally found it a bit overwhelming with the mixture of really basic practical stuff combined with more advanced circuit theory, but it's no doubt popular for a reason.
Another standard recommendation is to buy one ARRL Handbook from each decade (I have 1988), the older ones have less advanced (hence more accessible) material. But reading the "Electronics Fundamentals" chapter is no substitute for Grob and Malvino.
More recently I've been dabbling with electronics again. Someone recommended Malvino's "Electronic Principles" (I bought the 5th Edition second hand), which I found much clearer for circuit theory than AoE. Sedra and Smith will probably be my next purchase but I doubt it should be your first.
Also, "beginner" could mean a lot of different things. And perhaps more important than where you're at, where do you want to get to? There's a world of difference between (1) soldering together someone else's design, (2) being able to understand why someone else's design works, (3) being able to piece something together from common sub-circuits, (4) produce your own design from scratch. And all of these will vary depending on the circuit type: analog/digital/RF etc.
http://nand2tetris.org/book.php
For analog electronics and PCB's, the latest list of books I found was this:
http://www.circuitstoday.com/4-great-books-to-study-basic-el...
Malvin's Electronic Principles, which I got for $2 on Amazon, was also much more readable than Horowitz and Hill. Another thing to know is resources are usually almost all hands-on or all theory. Gammel's Contextual Electronics course that bradfa links to below was said to be in the middle somewhere. Also, if digital, you might want to make a note of "High-Speed, Digital Design" for later along with some book on verification either formal or "design-for-testing." Some people also do FPGA cookbooks and such if they're working with them. For RF, most people have one by ARRL or something whose name I can't recall. Finally, for electromagnetic compatibility testing, the great article and conversation linked below has a book in it.
https://news.ycombinator.com/item?id=15440411
Hope some of this helps.
https://contextualelectronics.com
Also, get some edition of Malvino's Electronic Principles. Easiest to understand book I saw looking into electronics.
https://www.amazon.com/Electronic-Principles-Simulation-Albe...
Also just found this. Use it as backup copy if you buy the book.
http://www.talkingelectronics.com/Download/Malvino_Electroni...
Still suffers from general problem with electronics books where I hardly know where to start on building real things. People have been recommending Chris Gammel's courses or certain kits for that, though.