I've been doing academic-type blogging since I was halfway through my PhD; it's been about 7 years now, and I continue as a non-academic scientist. My main advice is, as many others have said, to just write. Keep at it, and you'll figure out the rest as time comes. Try to bang out a post a week at minimum and things will fall in line.

I personally found that--in contrast to what many suggest here--I have almost no interest in explaining anything to non-specialists. Instead, my blog is mostly (or most successfully) a forum for me to work through ideas. Many times I will have a small nugget of a thought, and I will make a blog post where I model something in a Jupyter notebook. A couple of times, these have turned into papers, so that's been very helpful personally. I am also making an effort to write about topics that I don't understand, highlighting where I'm confused, as a way of getting my thoughts in order (and not all of these things may be understood by any scientists).

One consequence of ignoring explanation is that I have no regular readers (as far as I can tell; I don't use tracking scripts), and posts aren't widely read unless I promote a post by emailing it to people that then put it on twitter or facebook or whatever; I don't use those myself. This isn't directly a huge problem for me (although more positive name recognition couldn't hurt), but it might not be what you're after.

If I was in grad school now, I would use the blog as a way of making high-quality, permanent notes of things that I learned, whether they're concepts, mathematical or computational techniques, literature reviews, etc. Give attribution where appropriate and don't share homework solutions (use your best judgement on exercises and maybe change the problem sufficiently if you really want to blog your homework. Or just ask your professor...). There is a lot that I've halfway forgotten over the years and my paper notebooks haven't all survived many moves, etc., and don't have the quality that I would have put into them if I were making them public. I am starting to do what I can to make good notes in emacs org-mode when I learn new stuff or need to revisit important things in my day to day work as a researcher, but it's tough. (The format of good digital note-taking isn't important; the practice is.) Grad school is basically about this, so making good notes (ideally with some illustrative, working code where appropriate) will pay dividends in your later work.

Good luck!