I want to write this guide mainly to help Demon Hunters though it will work for anyone and is the best for anyone. It's mainly the same as vSully's guide (and he includes a video so you can see it in action as a Barbarian).
At the end, I was getting a consistent 375-400k gold per hour. Nowhere else got anywhere close.
Where and What?
Hell Mode. Act 3. Master 1. Choose the quest to kill Azmodan.
You will start by porting to Arreat Crater Level 1. Make a bee line all the way through the Act until you ENTER the Heart of the Cursed. At this point, port back to town and then go to the Core of Arreat. Run through there until you get to the entrance of the Azmodan fight. Don't kill Azmodan - he drops very little gold and it's not worth the time.
Now, star over. If you went to all the areas I said, the first area will have reset and you can clear it again keeping your Nv stacks.
What to Kill?
You'll want to kill only the elites and bigger enemies. Bigger enemies means Heralds of Pestilence, Phase Beasts, Golgors, Malachors, and Demonic Tremors. They almost always drop gold. Everything else rarely does. Elites of course always drop gold so they're worth killing.
You'll also want to stop and open all chests and demonic vessels as they always have gold as well.
Of course, you'll want gear with Gold Find on it. There are lots of options and if you can find others to give you gold find items, you can get quite a lot of it. The maximum gold find you can have on your character through items and Paragon levels is 300%. You can check this on Easy. The extras from Master 1 and Nephalem Valor will add to the 300%. Thus, the max you can have is 435%.
Generally, any item with gold find is better than anything else as long as you do enough damage to kill things quickly. You should be fine with anything more than 100k damage in the character screen and that's easy to get (I ran with 160k and also prioritized move speed and pickup radius).
Here you go. First and foremost - the most important thing to learn that I didn't discover until I had already lost hundreds of thousand of potential drops - DO NOT USE THE FERRET COMPANIONS. "But why!? They give me 10% gold find and pick up my gold for me!" Well, as it turns out, the gold the ferrets pick up DOES NOT COUNT TOWARD YOUR TOTAL. Yup. Don't make the mistake I did. This inspired me to write this guide.
Bola Shot - Imminent Doom (There's not much use for this, but it's better than the alternatives for non-hatred abilities and it's useful against the illusion elites)
Rapid Fire - High Velocity (Use this to kill everything quickly)
Shadow Power - Night Bane (Heals you to help kill reflect damage elites and gives you a little extra hatred so you can go longer)
Vault - Tumble (If you're moving, you should be vaulting)
Preparation - Focused Mind (More vaulting)
Strafe - Stinging Steel (Or drifting shadow if you don't have a lot of crit. Use this to generate preparation on the run if you're out. Otherwise, never use it)
Night Stalker (More discipline means more vaulting)
Vengeance (Extra base hatred so you almost never run out and more discipline means more vaulting)
Tactical Advantage (The most important one - Wait 2 seconds in between each vault)
Vault through the areas until you get to an enemy you want to kill. Kill them with Rapid Fire, then keep vaulting. Use other abilities as described above.