The Dwarves take a bit of getting used to before they become an effective army. For one, they are unlike any other army. Two, they have a wide range of troop types to choose from when creating your army. Below are discussed some of the troop types, and how they can effectively be used in a battle.
One of the most effective deployment strategies is the "Castle" defense. In this defense, you cluster your units together in the middle of your deployment zone, making sure that you have a few units facing off to the sides against infiltrators. Put your war machines and crossbowmen in the middle and any other large groups up near the front. When the battle starts, try to keep this formation tight at all times, especially if your opponent has taken flyers or infiltrators. Even if he engages one unit with his troops, you should have another one within range to help out in a hurry.
Another option you can take is the "Steamroller" strategy. In this option, you take a large unit of hard-to-hurt troops and march them forward towards the enemy, keeping the softer units behind it for cover. When you get far enough out onto the table, then branch out the others and go at it.
Now, to talk about the troop type themselves.
Heroes and Champions
If you haven't figured out how to use these yet, go read the Rulebook again.
Runesmith
Extremely useful, especially if taken as the higher levels and ocassionally with the Anvil. Always take the three Runes of Spellbreaking that he allows you to take. Without them, you are more susceptible to magic.
Longbeards
Longbeards are one of your 'elite' regiments, capable of taking on most other units in hand-to-hand. They do have a few disadvantages however. One, they are 15 points per model. Two, slow movement. Three, no missile weapons and weak armour. They are extremely useful however, for enemies with a higher Toughness because of their Str 4. They just need to get their first. A Golden Sceptre given to a character with the unit will help out with many things, turning them into an irresistable force.
Iron Breakers
Same as the Longbeards, but more expensive and harder to hurt. If given the Golden Sceptre and the Standard of Shielding, they can have a 1+ save! I prefer these to any other elite unit, since they cannot be hurt by most troops, and even the ones with Strength 4 have a little trouble.
Hammerers
Same as Longbeards, but always give them the two-handed weapons. If they get into hand-to-hand with anything really big, they still stand a good chance of hurting it badly.
Dwarf Warriors
Your standard troop type and exactly the way you should use them: standard. Field as many as possible, filling any gaps in your army with other troops. If you prefer the better elite units, think about putting in a few small units to make a run towards the corner points to take away territory from the enemy.
Dwarf Crossbowmen
Your missile troops, capable of even taking down Chaos Knights or other such nasties. Good range, decent armour, and moderate hand-to-hand skills makes these guys one of the better units in your army. Treat them exactly as you would with Dwarf Warriors.
Thunderers
Basically for the same points cost of a Crossbowmen you get a crossbowmen with reduced range and a higher save modifier. I would suggest only taking these in battle against Chaos, where the high save mod. helps out a lot.
Miners
Hand-to-hand troops with two-handed weapons. A little light on armour, but their points cost allows you to take many more of them than usual.
Troll Slayers
What can I say? Cheap, expendable troops that don't break. Very good for the points, but you have to make sure that you can get them across the table to do some damage. Use another unit to screen them and then swing them around right into the foe. About the weapons options: It is a good idea to equip them with two-handed weapons, especially when you are fighting against things with high Tougness/ low armour saves (i.e.Chaos Knights, any monster). The ability states that their Strength (INCLUDING weapon modifiers is always equal to the opponent they are facing. So, in other words, since they have Strength 3, with two-handed weapons they wound things with Tougness 3 or less on a 2+, Toughness 4 on a 3+, and Toughness 5 or more on a 4+. With two weapons, they will most likely always wound on a 4+, unless the opponents Tougness is 2 or less. And it doesn't matter that the Slayers will go last, because they would anyway because of their low Initiative. IF you are taking them as a task force to destroy creatures with a Toughness higher than 5, then equip them with two weapons, so they at least get the extra attack.
Gyrocopter
One of the better war machines, since it can fly quickly and its template weapon offers no save for armour. Use this against densely packed units of expensive troops (put the Rune of Disguise on it so it doesn't get shot down first) and you will make up the cost of the machine on the first volley. It is also useful against skirmishers, which the dwarves have trouble hitting because of the -1 to hit. The template doesn't care about minuses.
Bolt Thrower
Though putting a Rune of Seeking on this and shooting down a flyer puts a glint in any Dwarf players eye, it is probably unlikely. First, you need to hit. At -1 for range, the Thrower will need a 5+ to hit, unless the creature is lagre in which case you need a 4+. Either way, chances are you won't hit. And even if you did, the bolt probably wouldn't do much damage. (Most flyers have 4 or more wounds. A really lucky hit could do it though) Using them against units isn't much better; you still need to hit, and only affect one column. Cannons do better, but are prone to misfiring. If you misfire a lot, try this out for a while.
Cannon
Works great against large units, heavily armoured targets, or anything with more than one Wound. It does misfire, so contemplate some Runes to help out.
Organ Gun
Total destruction. That's either you or your opponent after you fire it. Though short-ranged, the extra flying time and bounce gives you a range that is rather formidable. When firing all barrels at once, spread your shots around a little, since the vagaries of the die roll could lead you to under or overshoot your target. Again, as with the cannon, some runes do nicely to help with Misfires.
Flame Cannon
Another template weapon. Very short range, but again, that doesn't matter much. With a couple of runes of penetrating, you have a small cannon with a template that can really put a hurting on a large unit. runes, runes, runes.
Stone Thrower
If you are good at guessing ranges, this is probably the weapon for you. Excellent range and a template can cause severe damage. Too bad there isn't a model for it yet.