Since the article sucked, I'll give the 2 best engineering advice I've received from 2 different senior engineers:
>Remember when you'd go to eat at a restaurant, and the kids menu has that game where 'What's the difference between these two pictures?' That is Reverse Engineering. You have a part that works, a part that doesn't work. What is different?
>"You just kind of figure it out". Not sure how to start/solve a problem. Figure it out. This means researching, doing math, proving, and testing. And as I've done this more and more, math is really really useful to prove things.