Most people interact with GitHub either with its website, a Git client on the command line, a plug-in in their favorite IDE, or the official GitHub desktop GUI.
The most recent version of the last one, released earlier this week, provides a cleanly designed interface for a few of the most common GitHub activities. But don't expect it to be a replacement for interacting with GitHub's site -- yet.
Version 3.0 of GitHib Desktop is a replacement for the previous Windows and Mac clients, for "a unified experience across both platforms." Launch it, and you can open, create, or clone a Git repository, either from GitHub or from any other Git-compatible repository.
Aside from cloning or adding repositories, the major activities in GitHub Desktop involve switching or creating branches, opening pull requests and committing changes, and performing merges. Branches can be compared against each other, and the changes for commits are illustrated in the same manner as GitHub's diff syntax. If you've used Git or GitHub integration plug-ins for IDEs, most of this familiar should be familiar to you.
The most glaring and surprising omission is integration with many features GitHub provides above and beyond Git alone. Issues, for instance -- within the GitHub Desktop interface, there's no way to browse existing issues in a repository, create new ones, or reply to existing items. Instead, you have to follow a link from within the program to the repository on the GitHub site. The same goes for repository wikis or graphs; you must go through the GitHub site to deal with them.
One minor annoyance, at least in the Windows version: If you browse for a directory -- say, to add a new repository from a local drive -- GitHub Desktop pops up the minimal version of the Windows directory-browsing dialog, which lacks the ability to browse to a directory by typing its name. The full-blown file/directory dialog, with quick links to common folders, is more useful.