Some thoughts on improving your handwriting
The three big keys to writing more neatly are:
1.) Slow down. I write quite quickly now, but being forced to slow down was the real key to improving my writing. Slow down while you're trying to improve. You'll build muscle memory and you'll be able to write quickly again in time.
2.) Buy a decent pen or pencil. Spend a dollar or two on a nice wooden pencil (find the lead hardness that feels right), grab a Pilot Plumix ($7), Pilot Varisty ($3), Platinum Preppy ($3), or a decent mechanical pencil (working on the thread now; <$10). You want something that will give you some feedback between pen/pencil and paper (grab a decent notepad, too, for a few bucks - thinking more about a thread for that, too!). That's my problem with ballpoints - I can't write as well because they tend to slide around too much on the page.
You want something that feels good in your hand. If it's nice to use, you'll find yourself writing more.
3.) Practice. I never really did pages and pages of individual letters. You can do that if you'd like, but I find it most helpful/fun to keep a sketchbook on my computer desk and write down song lyrics/quotes/lists of games, music, etc. I'm interested in. It's a very natural way to practice your writing and drawing.
I was thinking more about how my writing changed and Pau mentioned to me that she really loves the way I write the letter "f". That's my favorite letter to write and I currently have 5 different ways to write it. So Pau's nice comment got me thinking...
The fourth over, my really loopy f, is the one that people always point out to me. And that was the first letter that made me think, "Wow, my writing is starting to look kinda cool..." I actually started writing it that way completely by accident. I press fairly hard when I write, and my handwriting used to be more compact. After I broke my hand, and was struggling to write, I couldn't keep my lines as tight, so I'd end up erasing lots of letters when my hand would slip. One day, I made something like my first really loopy f and I thought, "okay, that's kind of fun..."
I think that's honestly the way to get started. If you're jotting down things all day, and trying out different ways to make certain letters (I do a Coptic 'e' now; I'm not totally consistent in how I write many letters, but that's the way I've made my writing distinctive. I replaced my more linear 'Y' with a loopy one fairly recently, and I think it looks really cool. Loopy letters look really nice with an italic nib pen. The loops show the thick-to-thin really well...), you'll probably find that first one that makes you smile. Then you'll start making your new, distinctive 'W,' or whatever, and you're off to the races. From there, you'll pick out more letters to experiment with, that will anchor your new writing.
I still try out new ways to write things all the time. I have a few letters that I don't think I write as well, and I've found ways to improve them over time.
For me, finding a way to make one distinctive letter, one that felt really nice to write, was sort of the big breakthrough. And it's still the letter that people point out to me as looking really cool. The process of improving your handwriting is indeed a process. You have to unlearn really ingrained habits and it all takes time. You won't go from chicken scratches to illuminated manuscript right away, nor will your writing smoothly evolve all at once. Play around with different letters and you'll find one that points the way to a new style. And when you find that letter that just feels really great to write, it'll make you want to write more, so you'll get even better, and find more letters that seem kinda cool, and so on...