Since you are new I'll give you run down of UD basics (since I'm rediculusly gosu with UD)...
THE HEROS
Death Knight: Usually the best choice when facing Night Elf and Human. A good all around hero for harassing as well as creeping. Death Coil is his bread and butter ability, acting as a healing spell, hero nuke and his best way to harass. Unholy Aura boosts your entire army with increased healing and speed to get around, which is always useful. Death Pact is probably the most underused skill, mainly for the fact that the DK needs his other abilities a bit more rather than sacrificing a unit for health. Finally, Animate Dead which is a interesting ultimate that is underused. Basically, you want to go Coil/Aura/Coil/Aura/Coil/Animate Dead or Aura/Animate Dead or Aura/Pact/Pact/Pact.
Lich: This is a hero you'll see very often used first in Undead mirror, and used second in almost all other matchups. Frost Nova is a great AoE spell and Hero nuke that does great damage and slows the targets affected. Dark Ritual is best used with a Rod of Necromancy to provide the Lich with more Novas. Frost Armor is a very situational spell that causes distractions from the Lich's main goal: Frost Nova. Death and Decay is also an interesting spell, that destroys trees and does percentage damage over time, a more situational ultimate. Find yourself picking Nova/Ritual most of the time, though some swear by a level of Frost Armor in between Novas sometimes.
Crypt Lord: The new hero to TFT, used mainly as a 3rd hero, but a good starter when matched against Orc. Carrion Beetles is the spell you want if you go Crypt Lord first. Pop those beetles out straight from corpses, cause they have no timer on them and work great when massed. Impale is an AoE stun with a bit of damage that goes in a line shape, the spell to pick when using the CL as a 3rd hero. Spiked Carapace is a defensive mechanism for the CL that reflects damage and adds armor. His ultimate, Locust Swarm is one you probably won't find yourself using very often. Good spell when your DK has no mana or you need to do damage fast. The CL is usually seen picking Beetle/Carapace or Impale/Carapace, but Beetle/Impale is seeing a bit more light as well.
THE UNITS
Ghoul: This little guy is quite fragile but does good damage, is cheap and great for surrounds. He harvests wood and recieves a huge boost at Tier 3 with Ghoul Frenzy that allows him to move and attack faster. You'll find yourself using this unit against Medium Armor units (Archers, Riflemen) as well as for hit and runs on Peasant lines.
Crypt Fiend: Your basic anti-air unit that is acts as a Piercing damage ranged attacker. He receives Burrow and Web at Tier 2, both are great skills to have. Burrow makes the Crypt Fiend dig underground where he has the "invisible" state and heals health rapidly. Find yourself smacking the Burrow key when you have a Crypt Fiend on low HP. Web is a disabler that brings air units to the ground so your Ghouls can hit them. The air can still attack but it can't move.
Obsidian Statue: Heals health and mana over time using a castable aura that drains a bit of mana every time. Basically works as a toned down fountain that has a little surprise at Tier 3.
Destroyer: If you get the Destroyer upgrade at Tier 3, you can use the Obsidian Statues to morph into Destroyers. This Tier 3 unit is a great anti-caster that does magic damage and has spell-immunity. It also has Devour Magic, which eats up any positive and negative buffs in an area, giving the Destroyer mana. This mana is used for Orb of Annihilation which adds 20- damage to the Destroyer and allows him to do splash damage. His last skill is Absorb Mana which takes the mana from a friendly unit and gives it to the Destroyer.
Abomination: Your Tier 3 melee unit does great damage and has high health. Pretty basic really, receives a "Disease Cloud" when researched that acts as a typical poison. Does damage over time but costs quite a bit.
THE ITEMS
Rod of Necromancy: This thing creates 2 Skeletal Warriors that are on a timer from any corpse. This means the corpses generated from your Graveyard, creep corpses, or even those Sheeps that you find walking around. You'll find yourself buying this item almost all the time since it works as a Mana Potion for the Lich, as well as a valuable creeping/harassing tool.
Dust of Appearance: Threw this in here cause it's often used vs NE. And if you're smart it's used in mirror vs. fiends or crypt lord. Click it and it coats units around your hero with Appearance Dust, rendering them visible when invisible for a certain amount of time. Great against that pesky Blademaster as well as hiding Archers.
THE STRATEGIES!! -
Sorry it took so long...
Mass Ghouls Tier 1 Push: Commonly used against NE where you skip your early tech and set up another Crypt pumping Ghouls. Can also be used against Human if you grab a Lich (hurts a crapload if he's fast expanding). CL works with Beetles vs. Human and maybe Orc.
Quick Tech Tier 3 with Ghouls: One of the most popular strats, this involves you going DK/Lich/Crypt Lord (pull out Lich/CL vs. NE if you need a stronger Coil, or CL if you're low on hero levels) and harassing as much as possible with DK while creeping with Ghouls. On Tier 2 all you need is a Slaughterhouse, a Lich and your Tier 3 tech. Frenzy Ghouls/Statues work well when jacking Night Elf Tree of Life or when attacking Peasants. Be prepared to defend your Tier 3 tech to the death.
Fiends: Commonly used vs. Orc, this can be CL/DK/Lich or DK/CL/Lich. Creep creep creep, defend until you have Tier 3. Heroes play a huge role in this as well as your burrow micro, make sure you have good positioning also.
Necrowagon: Probably only used vs. Orc simply because Elf has Wisps and Human has Dispel. Spirit Walkers aren't very common meaning you can just overwhelm them with Skeletons if you play your cards right. DK/Dreadlord or DK/Lich, don't tech to Tier 3 too early.
Mass Gargs: Used commonly vs. Nightelf and UD. Gargs are great for harassing workers as well as being good scouts for expos (and potentially destroying them). This can make your opponent go nuts, just make sure you can defend yourself at home.
Fast Expansion: Don't see this much but it can lead to a Tri-Crypt attack. Fast expansions work best with a Dreadlord using sleep or a DK coiling to minimize damage to your Ghouls. Sleep surrounds are cake thanks to your assload of Ghouls.
Frost Wyrm tech: Don't see this much.. I'd say Frosties are best in FFA or accompanied by Fiends if you have an expo. They cost a LOT to make and if you're opponent scouts it you're pretty much screwed.
Mass Banshees: Well.. it's incredibly hard to pull off but if you can do it then you've pretty much secured the game for yourself depending on what you're Possessing. Otherwise I highly advise against this.
Abomination with Necros: A bit strange but Unholy Frenzied Aboms are really strong, try to avoid Dispel as much as possible because Necros blow vs. Dispel/Wisps.