The example is clear:
$ cd $GOPATH/src/github.com/user/hello
$ git init
You do initialize the repo within your project 'hello'.
That way:
- you can push it to your GitHub repo (that you need to create first on GitHub, empty): - git remote add origin https://<user>@github.com/<user>/hello
git push -u origin master
 
- your go project is "go gettable" - go get github.com/<user>/hello
# that would clone and compile the project in `$GOPATH/src/github.com/<user>/hello`.
 
The .git you see outside hello (on the same page) is for another project:
src/
    github.com/golang/example/
        .git/                      # Git repository metadata
    hello/
        hello.go               # command source
Here, the project is 'example' and include several packages, including the hello one.