I'll second the recommendation of getting a pen you really like. The next step is going to depend on your boredom threshold. If you can do it, find an article

I'll second the recommendation of getting a pen you really like. The next step is going to depend on your boredom threshold. If you can do it, find an article or two, ideally a few pages each, and copy them word for word in longhand. The goal of this exercise is for your brain to get bored enough to naturally push you to go faster. For legibility, add in that if it's unreadable by your partner/friend, you have to redo that article (and not pick another article: that would be too interesting :). If you have more time, handwriting a nightly journal or regular letters to someone is a more pleasant way to achieve the same goal. As writing more than a few words at a time becomes rote, it will naturally get better and faster.