Generally, this will be by pointing out "I was introduced to you by someone you trust, which is why you've read this far. I clearly have the capabilities required to ship a game which will sell a lot of copies. I have lined up a team which has done this before, professionally. We have produced some early artifacts which suggest that we're capable of executing on this in a more-or-less professional fashion. Give us a small amount of money now, plus more if we hit some milestones, in return for the lion's share of our profits from this venture."
The true answer for "How do you get a publisher given that you're an enthusiast who hasn't worked in a professional capacity in the gaming field before?" is "You don't, unless you already have a hit on your hands."