The idea is simple…
Buy a sturdy college-ruled notebook dedicated to the relevant class. (I use the 100 page, 1 subject, college-ruled Stasher by Roaring Spring, but many people also swear by the Black n’ Red.)
Buy a good pen. (Nothing beats a black uniball micro 0.5mm.)
Take your notebook and pen and go to the most relaxing, meditative, non-distracting place possible. The deep stacks of the library is okay. Hiking 30 minutes into the woods or onto the dunes overlooking a windswept springtime beach is even better.
Spend 1 – 3 hours working out your thinking on the task at hand in the notebook. Spend the last 20 minutes carefully summarizing your results on a clean page that you mark with the date and a title.