Basics
Tomb Kings cannot March. Outmanoeuvre them.
Only two characters in the book have a chance of standing up to a Vampire Lord (even a strong Vampire), and even then they need a bit of luck. Challenge them, kill them and overkill for crumble.
Army Special Rules
Nehekharan Undead: Same as Vampire Counts Undead.
Battle Standard: Same as Vampire Counts Battle Standard. If present, eliminate to speed crumble.
Arrows of Asaph: Tomb Kings never modify their BS when firng. Only effects that directly change BS affect Tomb Kings missile units. This means you can't hide behind cover or anything, and closing is even more import, because range won't save you.
Animated Constructs: A special rule for the giant animated statues the Tomb Kings use. They have a 5+ Armour Save and -1 crumble, but can only regain 1 Wound per phase. Use this to damage them at your leisure, knowing you are in no hurry because of slow Wounds restoration.
Heirophant: One Liche Priest (Wizard) in the army must be the Heirophant. He must use the Lore of Nehekhara, and grntas his unit Regeneration (6+). If he dies, it's like our General dying, but Tomb Kings don't have the ability to use back up Heirophants.
Entombed Beneath the Sands: A unit with this special rule in reserve can place a counter anywhere on the battlefield, further than 1 inch from Impassable terrain or models, and then rolls the Scatter dice. If they land in terrain, off the board, or on models, they roll a D6 to see if they are a)destroyed b)placed by opponent or c)placed back in reserve. However, they cannot charge in the turn they arrive. You should be able to divert a unit to deal with a EBtS unit, because the units that can do it aren't a threat if you act quickly. There is a magic banner that grants this rule to a unit worth up to a certain points level, 175 I think.
Units
I'll start with special characters, as they are often present whenever points allow. They are almost compulsory for Tomb Kings to be competitive. Remove them and you have a much better chance of winning.
Special Characters
Settra the Imperishable: The most powerful (and expensive) character in the book. He is a Level 1 Wizard with Nehekhara, but this is so they can reflect his fluff and have no Liche Priests and still have a Heirophant, or if he's used up too many points for a Liche Priest, as he is a special version of a Tomb King (combat Lord).If he is used as Heirophant, this means you can eliminate the Heirophant and general in the same turn, making it easier to destroy the army. He, like all Tomb Kings/Princes, has a rule called My Will be Done, which grnats his unit (not mounts) his impressive Weapon Skill 7. His version, The Will of Settra, affects all units within 6 inches, so you have to destroy him otherwise you'll be facing Weapon Skill 7 Core and Special. His Crown of Nehekhara gives him 18 inch Inspiring Presence.
He and his chariot, which he must use, have a 4+ Ward Save, and his Chariot of the Gods does D6+1 S5 Impact Hits. His Spear of Ptra weakens opponents by giving them -1 To Hit each time he causes an unsaved WOund on a character or Monster in close combat, and gives him Always Strikes First and Flaming Attacks that allow no Armour Saves, making him extremely deadly in combat. The Curse of Settra will mean that the model that kills him will take quite a lot of hits after killing him. However, a lack of Magical Attacks means that a Cairn Wraith or Tomb Banshee can tie him up (in a challenge, of course). Terrogheist however is easier. He will be in a Chariot army so watch out for the other units.
Queen Khalida: Special Tomb King (Queen). Always Strikes First, staff containing a Bound spell that causes damage, and increases her unit's BS to 3. meaing Arrows of Asaph is now Always Hits on 4+. Also Hates Vampire Counts. se Ethereal character, Vampire Lord or drown in bodies. Her archer unit also has Poison, so be careful with your monsters. Death snipe.
Prince Apophas: Special Tomb Prince, but operates more like an Assassin. Sent back to the land of the (un)living to reap souls for the Nehekharan God of the Dead, he picks a target character at the beginning of the game and re-rolls failed rolls to Hit and to WOund against that target. He flies, has Regeneration (4+), a Breath Weapon and explodes on death. However, he can't join units, so just send Hexwraiths or a Spirit Host after him. He has Entombed Beneath the Sands as well, but as usual this has the problem of no charging on the turn he arrives.
Ramhotep the Visionary: Special Necrotect. Bonuses to Animated Constructs and Frenzy and Hatred to unit, but not that impressive. He also grants the ability to re-roll failed Armour Saves to a random Animated construct unit. Bait him with Wolves and outflank with Grave Guard.
Grand Heirophant Khatep: Special Liche Priest. Loremaster Nehekhara and can re-roll any casting result, including Miscast. Either you'll be able to Disepl him or he'll kill himself, which the Tomb Kings can't afford. Focus your Disepl dice on his spells. Death snipe him. Also has a special Dispel Scroll that can harm the caster of the spell that it dispelled, but it's on a 6, so I would just leave it out of your calculations.
Arkhan the Black: Special Liche Priest. Death Wizard, and is not forced to change his Lore of he becomes Heirophant. Level 4, but one of the Books of Nagash gives him Level 5, meaning he has 5 spells and can only lose Wizard Levels by losing his book. This means the player might be braver in 6-dicing spells, as 'lose Wizard Level' miscast results won't apply to him as much. Each unsaved WOund he causes in close combat restores a Wound to his unit, so make sure he's only fighting what you've sent to destroy him, as chaff will just rejuvenate his unit. He can take a flying chariot. Stop him, as he can be the Heirophant and restores his unit. Ride through with Hexwraiths, or Scream.
Tomb Kings: These are the generic Lord characters, with an almost identical Hero version called Tomb Princes, different only because of -1 Weapon Skill and -1 Strength on The Curse (causes damage to the model/unit that killed it). They are Flammable as well, so Hexwraiths will laugh.
They have a rule called My Will be Done, which grants their Weapon Skill to a unit they are in (not mounts). This means that one or two Tomb King units will have WS 5/6, without magic. However, apart from 1 more Wound, they have an otherwise worse profile than an equivalent Vampire/Lord.
In addition, a Tomb King (or special version) will often be the General, so killing him will mean that if you manage to kill the Heirophant (see below) the effect will be slightly more serious.
Liche Priests: Lord High Liche Priests, Hero Liche Priest. Generic casters. Light, Death, or Nehekhara. One must be Hierophant. Grants Regeneration (6+) to unit. However, must take Lore of Nehekhara (weakest of the Lore choices they have, but other non-character Liche Priests can take Light or Death) and if dies army crumbles. Like us, but no back up caster abilityRegular models have LD5 and Animated Constructs have LD 8, so crumble won't be an instant win button, but can be devastating if the dice smile on you. It is a good idea to try to kill the Heirophant, removing a Wizard (who might be the only Nehekhara Wizard in the army, shutting down the healing) and making it so that some Tomb Kings die every turn, making it slightly easier to win. In addition, if you can get a character to crumble (unlikely) then you've killed 200+ points for 'free'. However, expect the Heirophant to be well defended. It is a good idea to go after any Liche Priest with the Lore of Nehekhara, in fact, because the Nehekhara Lore Attribute restores D3+1 Wounds to a Nehekharan Undead unit that has been successfully targeted by a Lore of Nehekhara Augment. Also it slows their army, if the Nehekhara Wizards have opted for signature spell (bubble, targets move 8 inches. Basically Vanhel's without combat bonus option).
Necrotects: Give Hatred to unit and Regeneration(6+) to Animated Constructs (Sphinxes and statues) within 12 inches. Kill to weaken animated construct units, and removed combat ability from units.
Core
Skeleton Warriors: Exactly the same as ours, but will be taken more often as no Zombies. Zombies chaff these well, as same role but cheaper.
Skeleton Archers: Bows. Arrows of Asaph means they never modify their BS due to cover, etc, to balance BS 2 to some extent. All bow units have this. Because no modifiers affect their shooting, cover and distance are useless against them (except 48 inch Gaze). Close as quickly as possible.
Chariots: Chariots, riders are hit on one die score lower than normal. Can be joined by chariot-riding Tomb Kings and Tomb Princes for My Will be Done. Have bows and spears, with two riders (character replaces one). Can be fielded in units. Destroy with Hexwraiths.
Special
Tomb Guard: Like Grave Guard, but can take Halberds. Chaff up.
Ushabti:
Animated Constructs. Expensive. Great Weapons or S6 bows. Chaff up.
Tomb Swarms: Poisoned Swarms with Entombed Beneath the Sands. Never considered them, so can't really comment.
Carrion: Similar to Ogres in Strength and Toughness but Fly, and Movement 2 when grounded. Clear with Gaze of Nagash or your own bats (either type).
Sepulchral Stalkers: Monstrous Beasts with a shooting attack that causes Wounds=Artillery dice result, Misfire D3 Wounds to unit. 1 die per model, S1 vs I, magical, no Armour Saves.
Necropolis Knights: Animated Construct Cavalry 3+ Armour, riders have Killing Blow and spears. Mounts have Poison. May be upgraded to have EBtS, and can be combined with Necrotects for extra abilities. Expensive for few attacks. Send Zombies/Skeletons.
Khemrian Warsphinx: Monstrous Animated Construct without Fly, but still can have Poison and Flaming breath weapon. Crew are 4 Tomb Guard with Spears and Killing Blow, or a Tomb King/Prince However, because My Will be Done does not grant Weapon Skill to mounts, this option wastes the King/Prince's main ability, and is therefore unlikely to be used. If used, however, use a Spirit Host to tie it up.
Rare
Necrosphinx: Flying Animated Construct with one s10 Killing Blow attack, and optionally posion. Spirit Host will do the job nicely.
Casket of Souls: Is a Warmachine (T10) with a Bound Spell that forces a Leadership Test on 3D6- Leadership to cause Wounds. 48 inch range, so keep Terrogheist/Mortis Engine/characters away. On 3+ it affects another unit. It keeps rrolling until no more targets not already affected within 6 inches. Only massive Wizard-containing units (Wizards to heal) will destroy it. Protected by 2 Tomb Guard with great weapons. If it is destroyed by an external force, it explodes. Miscast or keep dying do not trigger explosion, just removal from play. However, T10 so excessive force will be needed. Focus Dispelling on it, Also, as long as there is at least one still operating, grants +D3 Power dice. This means that eliminating it will also weaken the Tomb Kings magic phase. Try Curse of Years.
Screaming Skull Catapult: Stone Thrower with magic flaming sones. Causes Panic Test if unsaved Wounds are caused. Skulls of the Foe gives -1 Leadrship. Warmachine, so use Dire Wolves, hexwraiths, Bat Swarms, etc.
[Tomb Scorpion: Monstrous Beast with Posion, killing Blow, Entombed, and Magic Resisistance (1). Spirit Host.
Hierotitan: Grants +2 casting bonus to Wizards using within 12 inches (not cumulative) and has Light and Death Signature as Bound Spells. Monster Animated Construct. Eliminate to weaken Magic Phase.
Bone Giant: Combat Animated Monster. Red Fury on first turn of combat (but continues until no more unsaved Wounds are caused, and can have either Great Weapon or S6 bow, but not enough shots for it to be worth it. Any high strength unit can deal with it.
When facing Tomb Kings, use cavalry, marching and chaff. Focus on characters, and take advantage of no marching. Heirophant must be declared, so you'll know where to look when you want to start collapsing his army Also you'll have somewhere to throw any Flaming attacks you have. Hopefully this is informative enough.
This is from memory. I can't remember the Heirotitan or that other giant monster, and anything else I missed or did wrong, I'll be happy to change.
Magic
The Lore of Nehekhara: This is the Tomb Kings unique Lore. The Heirophant must have it. Lore Attribute The Restless Dead grants D3+1 Wounds to Augmented Nehekharan Undead. Animated Constructs only get 1 Wound per phase.
The signature spell grants an immediate normal move to the targets, and while it cannot move units more than once, it can be cast more than once to get The Restless Dead. because of this, concentrate on Wizards who switch to this spell, as they will be trying to keep the army moving quickly.
The other spells have effects such as Extra Attack/Multiple Shots (2X), Killing Blow, or KB on 5+ if already, vortex spell, and hexes.