You can get your GitHub OAuth token in your GitHub settings in the developer settings tab. Remember to get a new OAuth token if you make it so yours resets every so often. After that, just run /condump and your server's console will be dumped into that repo.
/condump will dump the console log (logs/latest.log) into the designated GitHub repo in the config.
/conwipe will clear the designated GitHub repo of all files.
Any errors are from incorrectly setting up the repo or config. If this happens:
Try to make a new repo but add a file with anything in it. Doesn't matter what's in it. For some reason, GitHub stopped some of my requests because of an empty repo.
Make sure the OAuth token is correct, especially if you're getting a bad credentials error.
Make sure the token belongs to the repo owner.
Make sure your server is allowed to access GitHub, as in a firewall doesn't prevent it or anything.