Looking for learning resources to teach the "principles" rather than "follow this" projects
Welcome to the Arduino world!

First I'd like to try to answer your question: (This explanation does not apply to his situation as explained in the comments, but, I guess, it's a fun and useful read so I'll leave it here)


  "You'll also need to add a 10k ohm resistor from ground to the switch pin that connects to the Arduino [...] it connects the pin to ground when the switch is open so it reads LOW when there is no voltage coming in through the switch". I understand that in principle I think, but why is it 10kohm, why do we have to connect it using a resistor when the switch is open, etc. (I see that we have to have a complete circuit and I'm assuming it is because the 10kohm is a "default" branch of most resistance with nothing else connected?)


I haven't seen your circuit but I think I know the deal here. The author is basically telling you to create a pull-down circuit. What this does is, what it says. It pulls down the voltage on arduino pin to GND. Now, why would you want to do that? I think because in your project, the author was reading analog values from that pin. He wants the pin pulled down because otherwise when the switch is open, the pin would be floating i.e. not connected to anything. Floating pin means that you will get random analog readings from that pin. Basically, if you don't connect that pin to any source/sink, it will act as an antenna. You will get noise. (You can actually use this to create random numbers for your arduino!) 

Now, about that 10kOhm resistor: Its depends on two things. First, if you put a low value resistor, then you will draw lots of current from the supply to the ground when the switch is closed. You normally don't want that, why spend energy more than you have to? So, you pick any big resistor that you can possibly pick. But how big can you really put there? This depends on the analog read pin's current consumption. Whenever you do an ADC (analog to digital conversion) a.k.a analog read, your pin sinks/supplies tiny amounts of current and samples it to determine voltage. Atmel datasheet says that:



As you can see, the good guys in Atmel already did some tests and determined that with the current Atmega328p (Arduino-UNO chip) chip, a source of 10kOhm internal resistance is sampled the best. (When you open the switch, the 10kOhm resistor is basically a 0V source with 10kOhm internal resistance)So basically, I guess, that's why the author used 10kOhm. Could you have used 20kOhm instead? Of course...

Now about the electronics book thing. The best practice with electronics is to both read and do. So, whatever book you pick, make sure it has examples and explanations that you can try. Don't buy a highly theoretical book with lots of math and physics. Don't use a simple do-this do-that book either. I can't provide you a single good book, because that's not how I prefer to learn. But I might have some good suggestions for you if you prefer to study like this as well:


Learn the basics or R,L,C. Study filters, energy, their differential equations etc. Any book, website will do. 
Use software and simulate theoretical/explanatory circuits. LTSpice is best. For bigger projects, something like MATLAB is better.


If you do that, you'll gain some insights on how things actually work.


Move on to transistors: BJT, MOSFET etc. What are they and how they behave?
Combine transistors and R,L,C to create some digital-analog circuits. How do you make a RAM cell? Can you make an arithmatic logic unit?


At this point, you should be comfortable with most elements of electronics.


Since you started with arduino, study RISC/CISC architechture. What actually is a microcontroller? 
Since you know software, try using assembly code to turn on and off some leds. This is where you meet software and hardware at the lowest possibly level you can.
Try to make your own microcontroller using FPGA! (I've done this -it was a simple and not-so-useful CPU but nevertheless it provided insight. You can invent your own assembly language!!)


At this point you should be able to understand most basic arduino projects.


Read atmega datasheets. 
Read Transistor, motor driver IC etc. any driver datasheet and search the terms on google. What do they mean?


After that you can do this:


Pick a project, and do it from scratch. Without, copying any circuits from the internet. Can you place atmega chip to work stand alone, away from arduino board? Can you use that and make for example a BLDC driver?
Pick a project and ask stackexchange. (Well, obviously). There are some really brilliant people here that are willing to help. Personally, I feel I'm learning better if I try to answer other peoples questions and ask questions.


I guess the downside/upside is you never stop learning. Electronics combined with software is a huge area of expertise.

So I wish you Good luck!