My youngest is left handed, and his writing is just trash. I have no idea how to help him outside of specific left handed writing tools (that I'm pretty sure don't help at all).
When I used to write more on paper, many moons ago, I'd turn the paper 90 degrees to the right. Many lefties curl their hands over. I never got that, I just turn the paper. The body has to compensate a little but much more natural for the wrist when writing for longer spells.
Come to think of it, I don't do it much at all now, have probably got workarounds I'm unaware of at this point. My notebook stays aligned with the desk. Perhaps a slight tilt.
Either way, experiment with moving the paper, not the wrist, and get smooth pens as mentioned elsewhere. Fountain pens from Parker used to be my go to. Gel or roller are fine though.
Good luck!
Edit: I also learned to write under the line, so didn't drag my hand through the ink. Probably due to fountain pen use forcing that. Back when blotting paper was a thing!
If you write with the same positioning we teach to right handers, the hand hides the writing, and if you use a fountain pen you just smear the writing before it has a chance to dry. So don’t: slant the paper, like 45 degrees counter clockwise, and position your hand above the line you’re writing. Somewhat. I’m not the leftie, I’m working from memory here.
The key idea is to keep the text visible, and keep the writing position relatively comfortable. Then it’s just down to training. Target a specific style, draw individual letters… write stuff while concentrating on the writing, not whatever you need the writing for (you can’t really practice and take notes for instance).
Mostly boring advice, that apart from slanting the paper probably applies to everyone. (Note: I also have terrible hand writing, grain of salt and all that.)
Also, growing up in Israel, where we write right to left, I don’t recall any of my right-handed friends having issues with handwriting.
It's traditionally written right-to-left, top-to-bottom.
Probably the same concept at play, but what helped me as a kid was getting one of those black Pentel 0.5mm engineering mechanical pencils (used to be $5 apiece or so at Staples) and using it to write everything as small as possible. On college-rule paper my lettering would occupy 25% of the vertical space while strictly adhering to the bottom line in neat rows.
Few teachers could read my writing without a magnifying glass, but they got their revenge by specifying essay lengths in number of pages. I had to do 75% more work to meet the page count.
I wasn't intentionally being an asshole with this-- in writing such tiny lettering it forced me to pay attention to clarity of my lettering to an autistic degree, otherwise my writing would be entirely illegible to the teacher and my work would be rejected.
I am left-handed and my handwriting is terrible, but my partner is also left-handed and her handwriting is very nice but she position her hands as described above to "pull", so clearly it can be done if you apply yourself.
She also hand writes a lot more while I am almost exclusively typing these days so practice definitely helps.
If I had to do it over again, I would probably force myself to write right handed. It should be possible to get used to it, but that would really be a choice they have to make for themselves.