How does this Barbarian build generate fury?

Solution 1:

This build worked prior to patch 2.0.

The listed build is out of date - Into the Fray has changed since that time and no longer generates fury on crit.

Simple!

Battle Rage - Into the Fray.

While under the effects of Battle Rage, Critical Hits have a chance to generate 15 additional Fury.
_{- Diablo Wiki - Battle Rage}

I don't know why, but the site your providing does not gives the true definition of the Skill. :/

It is a very common way (if not the most used) to build fury as a barbarian. In fact, Most High-end barbarian players will stack AS (attack speed) as their priority stat. The Goal is to hit as much time as possible. With Whirlwind, the tornadoes of Sprint - Run Like the Wind and Overpower - Killing Spree, You hit so much often when in crowded groups of enemies that you generate tons of Fury. Spending it is also very important, this is why spamming Overpower, Battle Rage and Sprint. Consistently generating and spending your fury helps you keep your Wrath of the Berserker as long as you have something to hit.

The Hammer of the Ancients - Smash stands only for those High health elites. It is also a very good fury spender.

Here is a very good article of different builds of the barbarian. It is a bit old but you can still learn plenty of things, such as the proper ways of Generating and spending fury.

Solution 2:

That build was used prior to patch 2 exactly as Sinity has suggested. However, with recent changes to skills, the build listed there will currently not generate fury outside of normal attacks.