How can I contribute a patch to github?

I don't want to fork a project, but I would like to submit patches for inclusion; should I do this on the issue queue?

How do I contribute to someone else's GitHub repository?

Go into the directory for your project. Add a connection to your friend's version of the github repository, if you haven't already. Pull his/her changes. Push them back to your github repository.

You should fork the project. In Github, this is very cheap. This way, you can push your changes how you want to your repository, and then make a pull request to have them included in the official repository.

You can then delete your fork after that.

If you don’t fork a project, that means:

you clone the original repo directly;
you cannot push directly back to it (because you are not declared as a contributor).

Then you can indeed use the issue queue to reference a patch.
If said patch isn’t too big, you can directly copy/paste its textual form.
If not, you can copy it to some pastebin site and link it from your issue ticket.