General Army Notes:
The most noticable thing with a Dwarf army is their resilience. Even their most basic units have 4 wounds! They still only have the average 3 attacks, which means that they must rely on their survivability to win a straight assault. The Dwarf army's small amount of selection in units makes it less tactically flexible than some of the other armies, but don't count out the units available.
Core Units:
Warriors: Warriors definitely form the core of any Dwarf army. You have to take two units (mandatory) per 1000 points in your army. This means, however, that you will already have 220 points taken up. Warriors need to get into an assault as fast as possible, where their high number of wounds and excellent save will give them an advantage over most normal units.
Thunderers: Their guns give a -1 modifier to enemy armour saves. Thunderers make a decent supporting unit for your Warriors, but with their 6+ save and only one shot per base they will not cause major damage while shooting.
Rangers: They have a special rule allowing them to pursue cavalry, chariots, and flying units, which goes a little ways in balancing out the lack of cavalry and the like in a Dwarf army. Rangers are a versatile unit, and though they don't have as good a save as Warriors, their ability to fire upon their opponents means they can whittle down a unit before charging. Rangers, in combination with a unit of Warriors, make a good unit to assault cavalry, chariots, and flyers because of their special rules.
Slayers: Slayers always charge on initiative and cannot avoid enemies with initiative. They must pursue or advance (if possible) if they are victorious in an assault. Dwarf Slayers never fall back to missile fire. They gain +1 attack per base against monsters are are immune to Terror. Slayers can deal out a lot of damage, but even with 4 wounds they are vulnerable without a save. Dead Slayers, however, give up no victory points - the catch being that Slayers still alive at the end of the battle DO give up victory points! You can take two units per 1000 points.
War Machines:
Cannons: Cannon shots give no save and have a 60cm range, making them excellent for supporting your units. Cannons are very vulnerable to flyer assaults, however, so you should support them with either a character or a unit.
Flame Cannon: Flame cannons are excellent at taking out small units or hurting larger units, but they only have a short range. Rolling doubles for shots means something unexpected has happened (11 and 22 destroy the cannon).
Gyrocopter: Gyrocopters' flying ability allows them to move around quickly and take shots of opportunity at units, but they are very vulnerable.
Characters:
Dwarf General: The Dwarf General's high Ld means he can give multiple orders with little fear of losing a command check. His +2 Attacks will aid a unit in an assault, but you have to be careful with your General, as he is your most important character in the army.
Dwarf Hero: The Dwarf Hero is most effective when lending his +1A to a unit and giving orders.
Dwarf Runesmith: A Dwarf Runesmith's ability to dispel any spell, with a decent cost, makes him a rather useful purchase for a Dwarf army. For a few points more he can ride into battle on an Anvil of Doom, giving him +1A and one dispel per game at 3+.
Special thanks to Dalkwave for his help on this tactical overview!