How do I (self) publish a pencil and paper game?
If your game doesn't need any materials (or those would be more easily to come by on their own, such as graph paper), I would suppose the elements of your game you're trying to ship would be the rules. Since you're not trying to distribute them commercially, the only real problem is to get it out there.
If I'm correct so far, here's what I'd do:
Pick a Licence
An important part for both you, as well as players of your game, is the licence you intend to release it under. A licence determines what you intend to do, and what people may do with it - for example, whether they may redistribute it, and whether they need to give credit to you.
If you're willing to allow remixing and redistribution, there are a number of tested licences available for choosing, and the GNU project provides some recommendations about what you choices. They are rather software-oriented, so you might want to have a look at the Creative Commons licenses as well, which work for every type of work, or specific game licenses such as the OGL (Open Game Licence).
This is an important step, seeing as some licences aren't revokeable, and depending how popular your game gets, you'll be on stable ground legal-wise. Even for smaller games, this step is worth reading into for a little bit. Of course, until you decide on a licence, your country of origin's default copyright laws will apply, but a licence will still be helpful with attribution of the original author, for example if you end up hosting it on some friend's webspace.
Launch a Web Page
The easiest, probably cheapest way would be to set up a webpage from where people would be able to download a version of your game, and possibly get additional information about it, such as errata or update information, and maybe even a discussion forum. This has a few advantages over any print-reliant method:

you will be able to publish new versions with no delay at all, and players will know where to get the latest version of the game
you save the costs of printing copies of your rules on paper, as well as shipping costs and effort for the finished products
you maybe want a webpage anyway at some point in order to advertise your game
even without a monetary interest and a free game, you can provide information on how to donate money towards you or the project easily
aside from providing written rules, you could provide videos or other media that won't work on print

Making a web page dedicated to your game (as opposed to a blog post in your [insert your probably unrelated topic here] blog) would likely be preferrable, as it will not only appear more serious, but also give you the possibility to adjust the features and layout of the page to your liking.
If you don't have any experience in making web pages, you could rely on one of many web services that offer free blogs and a user interface that doesn't require HTML or programming skills, or find a friend or person online to put one up for you. There are too many possibilities to name them all, and more specialized communities at that.
Of course, asking a professional web designer would be a possibility if you're willing to spend the money.
Advertise your Web Page
Once you have your web page up and running, you probably want people to find it. I won't be getting into much detail here since it's not directly a part of your question, but advertising it on social media, your local game stores, local and online playgroups that play similar games (as you mentioned Go), general online game communities, and friends are general good starting points in my experience.