I went through this (and solved it with this group's help
) a few years ago.
Apparently the thread that I started to ask for help is now archived, but the key is to wire in the relay like Don says so that not only are you using proper gauge wire, but you're also no longer pulling all the fan power through your fuse box. Before I rewired my fan, I blew the first ignition switch, and subsequently melted the fuse that was added when the ignition problem was fixed.
I guess a fan just doesn't have to run as much in North Dakota as it does in Texas or Nevada - it's the only reason I can think of for using such a small gauge wire - I think I rewired mine with 10 gauge for the power circuit to the fan.
I can't access archives now, but if I can find it, it will be a good supplement to get you through this.
One thing that helped me was having a multi-meter (I'm also an electrical systems neophyte) - I was able to test continuity and function for the wires and switches I needed to use, and also understand what exactly a relay does.
Good luck - once you locate all the places you need to connect the wires, it will go quickly!
JLW