TL;DR
The Dwarfs are a slow-moving, hard-hitting faction with a focus on artillery and heavy infantry. Although they suffer from lack of access to magic, their high armor and leadership makes their units tankier than everything besides Chaos, and they’re second only to Skaven in the raw destructive power of their artillery. Access to the Underway gives them better maneuverability in the mountainous regions you’ll probably spend most of your campaign in.
Early Game Strategy
Regardless of which Dwarf campaign you’re playing, you’ll mostly be up against the Greenskins in the early game, maybe with a little Skaven mixed in if you’re unlucky. You won’t have access to your best units until the late game, so you can either try to rush your enemies with Tier I-II troops or hold the line until your settlements rank up to Tier IV-V.
Upgrading settlements is crucial, but Dwarves have a poor base growth rate and very few ways to increase it. You should always use the growth commandment when possible and prioritize growth buildings: the +15 growth quadruples the growth output of a level 1 minor settlement.
Army Composition
The typical dwarven army wants to deploy a hardened front line to protect a punishing back line of artillery and ranged units. In the early game, you’ll have to make do with 4-6 Dwarf Warriors with Quarrelers, Rangers, and/or Thunderers as your ranged damage and a handful of Grudge Throwers to back them up.
In the late game, your highly armored and nigh-unbreakable infantry can hold the line against multiple armies while you take the enemy apart with Grudge Throwers and Organ Guns.
Infrastructure
While the Dwarves aren’t exactly poor, they have a harder time cheesing their economy than the High Elves or the Dark Elves. Being an Order faction, try to take advantage of friendly neighbors to get trade deals going. You can give yourself more breathing room by seizing lucrative settlements like Mount Gunbad or Black Crag.