No name associated is quite easy to do technically.

-> Start a new dummy email for the anon user

-> Sign-up for a blog on Wordpress etc.

-> Start writing

However in practice it is really tough to stay anonymous, depending on how hard someone tries to find out your identity.

-> If you have a static IP address it can be traced back to you, may even be possible with a dynamic. Also its easy to trace using your hostname.[0]

-> Its really tough to keep personal information disconnected even in the smallest part. eg. people usually use similar nicknames online; you may tell your mom/family/friends about your new blog and they leave a comment;

There are tons of examples of how to blow your anonymity; but it can be done, you'll just have to be really careful if you don't mind the anonymity to go away at a future time.

[0] https://wtfismyip.com/json

It's not too hard to write anonymously. There are linux distros like tails https://tails.boum.org/ which can get you on the internet, then just go to whatever blogging site you want and write. Hardware-wise there is the gluglug-x60 http://www.fsf.org/news/gluglug-x60-laptop-now-certified-to-... but almost any thinkpad from the last 5 years will run linux well enough.

I'd use fictionpress or a Wordpress blog for this purpose. I use both, and the Wordpress blog because the story is... well, not exactly your daily run-of-the-mill story.

If you're looking for distribution, I would suggest just creating pen name accounts and writing under that.