Add a .nojekyll file
To deploy a static site exported with next export onto GitHub Pages, you'll need to add an empty file called .nojekyll to your out directory.
This is because GitHub Pages will by default ignore any files and folders prefixed by an underscore (like _next), as documented here: https://github.com/blog/572-bypassing-jekyll-on-github-pages
If your github page is a "Project Pages site" (rather than a "User and Organization Pages site"), you will need to perform the following step. (You know it's a "Project Pages site" if your URL looks like https://{username}.github.com/{reponame}. See this description for information about Project vs User & Organization Pages).
The extra step is to set a configuration in next.config.js. If you don't yet have that configuration file, you'll need to create it in the root of your project directory (next to package.json), as described here.
You will set assetPrefix in next.config.js to the name of repository like this:
module.exports = {
// some configuration
assetPrefix: process.env.NODE_ENV === 'production' ? '/{reponame}' : '',
// another configuration
}
Alter link URLs
You will also want to alter link URLs, because otherwise it will lead to 404. See this discussion: https://github.com/zeit/next.js/issues/3335
Pushing to GitHub Pages from a Subdirectory
For more info on pushing to a gh-pages branch with a certain directory (like the default out directory), see here: https://gist.github.com/cobyism/4730490