General Army Notes:
The Undead army contained in the Warmaster rulebook is a Khemrian army list, meaning it centers on Skeleton units. The Undead have some unique special rules that are quite useful. Undead have no -1 penalty to orders for enemies being within 20cm, balancing out the rule that they cannot charge or evade on initiative. Undead take no -1A penalty for Terror, and are never Confused. This combination of special rules means that the Undead army will advance in an almost implacable manner, and stand up well in an assault.
Foot Units:
Skeletons: You must take two mandatory units. Skeletons are rather cheap and form a good core for your army, especially with their special rules.
Skeleton Bowmen: Skeleton Bowmen are very useful in a screening role, where their missile fire can soften up the opposing army before a charge, and the Undead special rules mean that they pretty much will not fall back.
Cavalry, Chariot, and Monster Units:
Skeleton Riders: Skeleton Riders give you a good, fast light cavalry unit that can be taken in multiples. Two or three Skeleton Rider units can cause havoc for your opponent when deployed together and used in a combined assault together.
Skeleton Chariots: Skeleton Chariots are useful in a supporting role, where their versatility allows them to either add supporting fire or extra numbers in an assault. Their speed makes them redeployable quickly, meaning they make a good tactical reserve.
Carrions: Carrion make a decent cheap assault unit, with their high speed (being flyers) and 4 attacks with charging. They can be used as a harassment unit or to take on weak to moderate units, or even to aid another unit's assault. They are good for assaulting war machines and artillery crews.
Bone Giant: The Bone Giant has a -1 penalty when trying to give it orders, due to its being dead and brainless. Even so, it can be rather useful at times, taking on tough units in an assault. But the high cost means that you can find some better buys for your points (such as 4 Skeleton units, 2 Skeleton Rider units, or a combination of them).
Sphinx: The Sphinx's 4 Attacks may at first glance not seem like much, but with its high number of wounds and excellent save the Sphinx can take a lot of damage. Remember, however, that if it is seriously wound (takes 3-5 wounds in a single turn), its stats with drop down to 2A and 3W. A Shinx can be useful in larger games, but in small battles your points are much better used for more Skeleton regiments.
War Machines:
Skull Chucker: Skull Chuckers cause confusion in wounded units on a 4+. The Skull Chucker's special rules combines with its multiple shots and no armour save makes this war machine very deadly, but it needs a supporting hero or unit to make sure it does not get destroyed by flyer assaults.
Bone Balista: You gain one extra shot for each balista behind the first, up to a maximum of three. Since you get two bases in a unit, the Bone Balista can be more useful than it seems at first, especially as short-ranged supporting fire, but its low resilience means that unless it is supported, it will be destroyed rather quickly.
Characters:
Tomb King: The Tomb King, being your general, should be protected at all costs. His magical power can be used for defence as well as offence - remember this in the chance that the unit your Tomb King is in might get charged.
Liche Priests: Two max per 1000 points. Liche Priests are pretty good Sorcerors and are the only form of hero you have in an Undead army. Their abilities as spellcasters and giving out orders mean that Liche Priests are very valuable to the Undead army.
Zombie Dragon Mount: The Zombie Dragon mount might seem like a good purchase for 100 points, but the 100 points is more useful spent on more units.
Chariot Mount: A Chariot makes a decent mount for a character, giving him a little more hitting power in an assault and some mobility.
Special thanks to Dalkwave for his help on this tactical overview!