You wouldn't even necessarily have to have a private repo - you have all of your assets on your own computer, run `jekyll build` (or whatever the command is for the generator you're using) and then it'll output all of the static files to a directory (in Jekyll it's "_site" by default). You then move the outputted directory wherever you want, whether it's github or your own server.
I'm not too familiar with walkthroughs, but for Jekyll I just use the documentation, which is fairly high level and easy to follow. I'm not familiar with any generators that aren't managed primarily through a command line. I think the only commands I ever use are `jekyll new` and `jekyll serve`. Aside from that, it's all git. Probably the biggest barrier would be learning the templating language (for Jekyll, it's called Liquid, and is covered in the docs).
IMO, the worst part about Jekyll is that it's Ruby. After you manage to get it installed, it's great. And luckily, with static site generators, most people elect to install the generator locally, and then copy the output to your server, so you don't have to worry about getting Jekyll configured on your server. I'd recommend github's guide for installing jekyll.