Based on your skill choices and the way that you are dealing your damage you may not need as much Fury as you think. Personally, most of my damage output comes from Cleave and I seldomly am spending fury anyway. However, if you find that your Fury is frequently low there are ways to beef up the generation. There are several runestones that help fury re-generation. Your bread and butter Fury generation is obviously going to come from your Fury Generating skills.
Fury Generating Abilities:
Bash with Unleashed - Generates 7 extra fury per attack.
Cleave with Reaping Swing - Generates 1 extra fury per enemy hit (max 7)
Ground Stomp with Foot of the Mountain - Increase Fury gained to 43 fury per stomp.
War Cry with Charge - Generates 51 fury when used.
Furious Charge with Stamina - Gains additional 8 fury for every target hit while charging.
Ancient Spear with Skirmish - Increase Fury gain to 38.
Fury Spenders:
Battle Rage with Into The Fray - Criticals generate 7 fury per hit.
Seismic Slam with Strength from the Earth - Reduces the fury cost. (Could be helpful)
Whirlwind with Eye of the Storm - Reduces the fury cost per second.
Situational:
Overpower with Momentum - Generates 7 fury per enemy hit.
Earthquake with The Mountains Call - Reduces fury cost to 40.
Passives:
Weapons Master - gives 1 fury per hit with Mighty Weapons
Animosity - Increases Fury generation by 10% and maximum Fury is increased by 20.
Superstition - Whenever you take damage from a ranged or elemental attack you gain 3 Fury.
No Escape - Killing an enemy with Weapon Throw generates 20 fury.
Unforgiving - Generates 2 fury per seconds (no degeneration) (This one is awesome)
You can also refer to this link for more skill stats.
This website may also help you out.
It's a skill that doesn't work with the usual cast and cooldown mechanic as other skills do. Instead it will activate in 15% of you getting hit by a monster. You'll see that the skill-icon will turn active, but then you'll have to manually activate the skill.
The time-window for activating the skill is also limited. After some time the skill will become inactive again if you didn't chose to activate it.
While it's different from other skills, I personally like the mechanic and the skill already helped me in several situations (surrounded by monsters, this skill can be some sort of "panic-button" that heals you and deals damage in the same turn).
Update: Also note that the skill doesn't have a cooldown. So if you're getting hit a lot, you can potentially trigger this skill quite frequently. Especially if you enable the "Provocation" skill-rune (available at level 52) which increases the chance of activation from 15% to 30%.
Best Answer
Take note that this is prior to patch 2.0. Into the Fray has changed since that time.
Simple!
Battle Rage - Into the Fray.
"While under the effects of Battle Rage, Critical Hits have a chance to generate 15 additional Fury." (source)
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 diferent 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.
Hope it helped! :)