Speaking only for myself, it took a few months of regular writing.

Like (perhaps) others, I had been forced to use them in grade school -- we were told that "it would improve our handwriting". It laid a foundation for fluency in cursive, but my actual handwriting was terrible.

However, when I came back to fountain pens (after a couple of decades), it was relatively easy to improve my script to where I'm happy with it. Having the "cursive" foundation probably helped a ton.

You can improve just by learning the right technique (how to hold the pen, how to write by moving the arm rather than the wrist) and learning the proper letter shapes. That won't take more than a couple of hours, and from then on you just get practice by applying what you learnt whenever you have to write something down.

I have improved my handwriting. It took a few months of consistent journaling with a fountain pen to find the "font" that worked for me. Now, I have different writing styles depending on how much time I can take. I use a broad nib for quick note taking because I don't have time to make it look "good", and a fine flex nib for when I'm journaling which I use to flourish things a bit.

Yes, I bought a cheap fountain pen together with a book I could improve my writing on.