How does one remove a barrel from a Winchester action. I have the desire and the tools, what I need is the knowledge.

You need an action wrench, and something to hold the barrel without marking it up.
I have neither, but I got away with, cutting a groove in a piece of hardwood so I could clamp the barrel in my wood vise, and then using an oversized adjustable wrench with padded jaws (heavy towel) to turn the action. On an old SMLE, I had to heat the action slightly with a propane torch, on a '92 Winchester, no heat was needed, it was easy.
BE CAREFULL!!
It is really easy to crush, twist, or bend the action!

I have built big sturdy action wrench and barrel vice.
I have put penetrating oil in the crack and applied a little heat to the barrel. I have applied 1000 foot pounds + hit the action wrench with the sledge hammer, and it is still stuck.

Then I make a relief cut with the lathe into the barrel right next to the threads, and suddenly, the barrel is only finger tight.

Hold it tighter, and get a longer handle.

"Give me a lever long enough, and a place to stand, and I'll move the world".

You did take the bolt out of the action, right?

Soak the thread area in Kroil too.

By "Winchester" do you mean a slab sided lever action?? If so you have no problem. The are not very tight. You will need an action wrench. I use a couple of pieces of 1" square stock bolted together like a big tap handle. For the barrel make maple blocks that fit snugly around the barrel. Put that in the barrel vice. You will need to keep the breech bolt in the action. Be sure the extactor is out of the way or you will destroy the barrel, receiver, and bolt. This is a real common brain fart. I have done it and know others that have done it too. THINK! Maybe put a wad of cardboard in there to prevent the bolt form going all the ay foreward. Once you have the barrel in the vice, install the action wrench. I use cardboard, like from cartridge boxes, to protect the receiver's finish. Make sure everthing is very snug, and give the wrench a rap with the heal of your hand. It will come right off.

what model of Winchester?