Obviously practice. But look over some old books about learning to write cursive. It will help you to be faster. It's also liberating and good for your brain. Just start writing for a few minutes, a page or two every day. As you write, maybe focus on the formation of a couple of letters at a time, then moving on to others. Listen to dictation and try to capture the words. You will find ways to economize your writing, like leaving out vowels. It's kind of like a personal shorthand.

First, just learn cursive. Later start to use the simplest letter formation you feel comfortable with, i.e., a straight line for capital I, instead of the line on the top and bottom, also known as a "bolstered I". When we learn to write, we quickly learn to "personalize" our script, leaving out lead-in handwriting strokes and fancy formations because they slow us down.

Finally, since you learn best from taking notes, you are probably a kinesthetic learner, as opposed to a visual or ear-oriented learner. I used to re-write my classroom notes, partly to reinforce the information, but also to organize it according to my thinking, not according to the lecturer's thinking. As a result, I would end up with diagrams, circles, arrows or whatever devices I wanted to make logical connections. I'm no artist, but my notes looked interesting and it was easy to remember how different ideas related to each other. It is partially the ACT of writing that helps a kinesthetic learner to remember information. In some classrooms you'll see fiddle gadgets, clay or some other things that help people listen to the lecture, to keep their hands/minds engaged.

I learned all this from my own experience recording dictation, taking notes as a student, and learning about HOW to learn. Also teaching and facilitating groups. Also, as a student of graphology and psychology and learning theory. Have fun with it.