Every individual has a different optimal method of learning. Some people prefer information presented visually, some are auditory learners, etc. The trick to teaching anybody is finding the way to phrase or present something in a way that "clicks." I've always had a knack for that: those moments when the lightbulb finally snaps on.

I typically try to identify their strengths and weaknesses in how they learn. What approaches will be ineffective and just frustrate the student? Which ones work? Perhaps most importantly, which ones haven't been tried yet? If I'm called in to tutor, I expect it to be a case where I can find a way to instruct more effectively than whatever methods have been tried before.

Critical thinking is a must. I prefer what some might call the Socratic method: whenever you are given a piece of information, you should ask "Why?" "How?" and "How does this fit in?” Learning a subject, for most, is best done when everything is presented in context; not just a random slew of arbitrary facts. Sadly, most students are taught mostly to memorize; a skill which is largely useless in independent learning.

It really depends on the student. Sometimes, they just need a push to keep going. Other times, they can get increasingly frustrated with a subject by "not getting it," for too long. In those latter cases, it's best to back off the current line of approach and try something different. If a student subconsciously learns to associate a subject with frustration, I guarantee they will become averse to it, and thus struggle. With me, there are always 5 other ways to attack any problem. I'd like to note that this is a very broad question. Reasons for flagging motivation can be many, many things. Each case is unique and requires a unique approach; I've just gone over two of the more common ones.

I'd find as many new and different approaches to the subject as it takes until something starts working. Mostly, I use my knack for explaining complicated concepts in simplified plain English, with real-world analogies.

My most common (but not only) approach is to have them read a passage as if the author were talking to them, verbally. We'll then discuss the flow of the "conversation" and what we think the "speaker's" intonation would be, and what they'd emphasize. In some other cases, it's as simple as explaining grammar, or helping to define some key words and/or concepts.

The most successful strategy is to find the student's strengths, and avoid their weaknesses. If they are poor auditory learners, we'll sketch things or I'll find pertinent videos, etc. They key is to be flexible; adapt, adapt, adapt.

It depends on the subject. Real-world examples of cool stuff are always a good idea. More importantly though, I want to disrupt any rut a student may have developed of trying to learn a subject in a way that is ineffective for them. It's frustrating, and feels like torturing yourself (I've been there). There is always time to step back and approach the problem from other angles of attacks; most of which my students are initially unaware of.

The best technique is to have a student explain a complicated concept to me, unaided, in complete detail. (This is basically the learn-by-teaching method, and its benefits are twofold). This is the fastest way to identify both weakness and strength in many different areas of comprehension.

Start slow. Start simple. Make sure that you answer the "What is the point of doing this particular thing?" question before they even put pencil to paper. “Big picture" concepts are the most easily learned for my students, and also, I find, the most rarely taught.

Firstly, I'll ask them and listen to them on what they think they need to improve on. A foundation of mutual respect is key, and is impossible without valuing a student's input. At some points, I will ask them to explain a complicated subject or problem to me, in detail. This, and working with the student in general, lets me identify weaknesses that students often did not know that they had. Likewise, I'll also find strengths, and emphasize those to the student. The worst thing possible in this case is to systematically tear down a student's confidence even more than it has fallen.

As I've stated in my previous questions, I am adept at finding myriad alternative angles from which to approach any problem. The first action is almost always to take a step back and re-analyze "big picture" concepts. Then, we'll try approaches that the student hasn't tried yet. Often, before we even get to that point, my way of explaining things plainly and elegantly will produce a "lightbulb" moment. My abilities to adapt and to effectively explain thing in layman’s terms are what make me an effective teacher, more than anything else.

It depends on the subject, but a pencil and paper is almost always useful. Along with that, a device with internet access is just as helpful. If relevant, I often like to use open-source media such as YouTube. (An example of this would be showing a large sponge filter feeding with dye injected into the water to show how it generates a current). For higher math, I highly recommend a graphing calculator always be on-hand. Though you can do pretty much any mathematical function online these days, learning how to use your particular calculator effectively and quickly will help a great deal in testing situations.