Secondly, I'm going to skip the mechanical recommendations (the 'how-to' stuff). There's a great book called _How to Take Smart Notes_ that a lot of folks here rep these days. I quite enjoyed it. _Getting Things Done_ is also good. Either book will help you in this regard far more than I could. Instead, I'm going to focus on emotional dimension.
Claim: you can't build a habit unless you 'cathect' to the ritual and the tools.
Thus, you need tools that you like using, that you connect with, and you need a place you enjoy using them in, and you need a time every day that is generally available for this practice.
(Note: a lot of people (myself included) are initially frustrated that they cannot bring themselves to like _very_ inexpensive things. If you happen to love cheap ballpoints and scratchy, acidic paper, you're very lucky; otherwise, you're going to be hunting for the perfect notetaking implements for the rest of your days. Adjust to this idea. If it helps, you may reflect that paying extra for nice paper and pens is a trivial expense, if they get you writing, because writing is important.)
So, first of all, get yourself a notebook that you really like. Some folks do a single-notebook thing, but I prefer a small notebook for on-the-go and a larger one as a 'thinking surface'. (As it happens, I also like _very_ large thinking surfaces, and keep drafting paper and a roll to keep it in.). Make sure the paper quality is reasonable. I'm particularly fond of the dot-pitch notebooks by Statology, and Kleid also makes some amazing products. So do Clairefontaine and Rhodia (and those are generally easier to track down.)
You're also going to need a pen that pleases you to touch and use. If you, like me, appreciate fountain pens, but don't want to spend a fortune, I'd recommend, for example, a TWSBI Mini, which will still run you about $70 USD. (Skip the TWSBI Eco at $40 -- it's worth the extra $30 for the Mini.) I also quite like a Platinum Plaisir at about $15, if $70 is too much for you.
Get yourself a bottle of nice ink as well (I recommend an Iroshizuku ink by Pilot).
Some other accessories that making writing a joy: a leather (or silicone!) inkblotter; a great playlist or, in my case, a public radio station that has an amazing show on at _just_ the right time every day; and maybe, if you're so inclined, a small amount of whiskey. (Emphasis on the 'small' -- you don't need to go full Hemingway on this one.)
Now, prepare the rest of the ritual. Remember, the goal is to trick yourself into spending a certain enjoyable amount of time every day writing, reading back, organizing, and reflecting on your notes.
And that's why you'll find me in my study, every day at about 8pm, talking a brisk walk around my mental garden. If you don't have a study, a kitchen table will do. If you haven't got that (I've been there,) find a nearby café that feels like home.
And that's how I keep notes in 2024.
P.S., if you find your handwriting is terrible, well, you probably need to use it more! Consider also calligraphy as a means of refining it.