I keep notes in a variety of ways, depending on what works best for the situation. Sometimes I'll use a physical notebook and pen, other times I'll use a note-taking app on my phone or computer, and other times I'll just use whatever is available nearby (a Post-It note, for example).
The most important thing is to find a system that works for you and that you're comfortable with. Experiment with different methods and see what works best for you.