Uhh, not quite. This is how you do it
"My best friend said, 'Like, yeah, and so he said, "Quote marks are dumb," like, so he went on and said, "my professor said that, 'John Barth was a bane on editors everywhere.' he said." she said,' my best friend said."
Got it? It's basically alternating " and ' (double and single) quotes. Go ahead and read some of John Barth's stuff, which uses this all the time, for some examples.