How does focus work in dragon age inquisition?

While Focus can be gained through dealing damage, it's very incremental and takes several fights to accumulate. If you want to use your Focus abilities more often, you'll need to learn combos. Combos are a form of class interaction. Each class has a set of specific CC/debuffs: Mages have Frozen and Paralyzed; Rogues have Asleep; and Warriors have Stunned. Each class has abilities that apply these debuffs, and each class has abilities that combo with these debuffs.

The latter abilities are called "detonators", you'll see them in your skill descriptions as "(something) Detonator". While you can detonate your own class debuffs, it just results in a basic combo that doesn't really do anything special and won't boost your Focus meter as much. However, if you pull off a cross-class combo (Mage Frozen into Warrior Impact Detonator, for example), you can deal tons of damage along with some special effects (the aforementioned combo does massive amounts of cold damage). You'll also increase your Focus meter much more.

You can unlock the second and third tier focus abilities through the war table. Its one of the inquisition perks.