My daughter's handwriting was usually discernible, but very sloppy. (Note that she is 5, so I am specifically talking about her ability to draw letters.) I noticed that most of the children in her class had much better handwriting, so I decided that it was time to address the problem. I just kind of assumed that they'd be spending hours and hours over the school year tracing letters, with an adult watching their form and correcting it, because that's what I remember from my early years of schooling. They didn't. In fact, they spent very little time tracing at all, and no time instructing them on form. They didn't even make sure each student actually finished tracing all the letters in their book. And it looked like my daughter either wasn't getting it by herself, or wasn't motivated to practice enough. So at the end of the school year, I showed her the letter positions (upstairs, downstairs & basement - as I learned it), and where each letter was supposed to go. It turns out, she didn't even realize that "n" and "h" were different sizes, so no wonder she made it so difficult to tell hers apart! We wrote down letters every day, with me sitting next to her to correct her form. I made her do each one over if any part of it was out of the lines, no matter how slow she had to write. I told her that she had to draw letters the right way before she could learn cursive, and that was plenty of incentive for her. Her handwriting is much more legible and hopefully that will facilitate her writing skills for first grade.
I think it's worth helping your child get it right. It will be a long time before everything is typed, and in the meantime, their handwriting needs to be good enough that an instructor can read it without too much difficulty so he/she can actually assess its content. Not to mention that writing with proper form allows a person to write faster. Tracing and practicing, with the oversight of an adult, is my best guess on how to tackle it.