For the best explaination that's free online I would look at the quick start rules
here.
Edit:
But basically the warlock starts with fury equal to their FURY stat. This can be used in the normal way of focus i.e. cast spells, boost, etc. Warlocks can also cast animi from one of their beasts within their control area. So not only do they have access to their spell lists but their beasts effectively come with extra spells.
Warbeasts are very different but similar to warjacks in operation. For anything you would spend a focus to do, (charge, boost, extra attack) the warlock can force the warbeast to do. This puts a fury point on the beast. Warjacks have a basic limit of 3 focus when allocated but warbeasts can be forced upto a FURY stat on their card. I've seen beasts with 5 fury before so this can be powerful. Warbeasts have two extra things to do with fury. They can be riled, which means you put fury onto the beast without having to hit things or run or they can be forced to use their animi themselves. Mostly you'll see animi with a range of self so it can only be put on the beast itself or cast by the warlock on themselves. There are animi with a range though and this can be used like a spell and put on a model within the range. When being forced to use animi instead of removing fury points you add fury points that equal the cost of the animi but again only up to the FURY stat.
At the beginning of the next turn you'll have a warlock with little to no fury on them and beasts with lots of fury on them. When a warcaster would replenish their focus the warlock can leech the fury off their beasts, but only up to their FURY stat. So they have to do a little balancing there. If the fury from the beast is too low, say 5 coming from the beasts onto a 7 FURY warlock, the warlock can leach from themselves by taking wounds and adding fury equal to the amount of wounds taken. But only up to the FURY stat of course.
If they can't take all the fury off the beasts, say 10 fury with a 7 FURY warlock, then there is the potential for beasts to frenzy and at that point my knowledge is limited so best look at the quick start rules.