I'll do my best to sum up what I do. I've never put this in words before.
My modus operandi involves building a mental model of what the student knows, doesn't know, and how they think about the problem in question. Usually I do this through targeted questioning, and watching faces for signs of confusion in a group session. e.g. let's say we're working on Newtonian physics. I might take a model car with occupants, roll it along a table, and ask what happens when the car hits something. From this I can judge whether the students understand momentum.
If their mental model is wrong, next you have to break it down. How to do this varies based on how committed they are to their model -- if you challenge their views in too dramatic a manner you can lose their trust and frustrate future lessons. For students whom are less committed to their incorrect model, it suffices to demonstrate a counterexample. Those who are more commited can require several weeks to shake their beliefs.
Actually teaching involves three parts: definitions, questioning, and experience. Definitions are KEY. You can build an entire lesson around a solid definition. For example: "speed is how far something travels every second" (or "in a certain amount of time" for the ones able to handle abstraction). Keep definitions few and far betweens and simple. Refer back to them often.
Next follow up with questioning: how can we measure speed? do we know how to measure the things in the definition? if something moved ten meters in five seconds, how many meters did it move every second? This has been covered elsewhere in depth. Don't overdo it though, some kids hate questioning. Just tell them facts.
Oh, be consistent. Use vocabulary consistently, don't throw around new terms, stick to one system of units, etc. Minimize distraction and confusion.
Experience is key to solidifying rules deduced from questioning. Roll that cart down the hill. Practice those factoring problems. Not everyone needs experience but most do. Experience can help break down incorrect mental models. As with definitions, minimize distraction. Experience one thing at a time until it is understood.
Finally, don't be afraid to go off on tangents. If a kid expresses interest in something, that means they will be focused and eager to learn it. You can teach almost anything to a student who wants to learn it. Motivation is everything.
I hope this helps. It's early in the morning and I'm writing this on my Kindle so it's probably rambly and missing things. I'll try to remedy that throughout the day.