I'll say some general statements about UD.
First of all, many units are fragile and can't take much damage. Orc units generally have high hitpoints, human units have high armor ratings and priests heal, while elves have their mountain giants and wells. So try not to engage with the enemy directly.
Corpses are very useful to the Undead. You will notice this when you use the Rod of Necromancy which is a great tier 1 item at your shop or when you are making beetles with the Crypt Lord. Always be aware where you can find corpses, such as the Graveyard.
Undead heroes require a lot of management to make sure they aren't focus fired and killed on the spot. Since I assume you are new, I suggest you use the Death Knight as your first hero and if you are willing, try to get a 2nd hero. When that hero is low on health, just coil him and he will be good as new. As for the deathknight your order will nearly always be coil/aura/coil/pact/coil/depends. I'd say pact because it's the safest. However, if you feel gosu and can make sure your DK is always safe, level 2 aura is a good choice at level 4.
I HIGHLY recommend you upgrade your first ziggaraut into a nerubian tower at the start of the game since acolytes are the most fragile worker since orcs can hide in burrows, humans can go militia and run off, and wisps are unhittable inside the gold mine and can dispell.
You should probably do the cookie cut strategy of using the DK fiends at tier 1, then moving on to Lich, statues at tier 2, and finally destroyers at tier 3. It's easy to do and works very well.
Finally, if you are up to it, hero nuke can work very well. For some reason, everytime I say that, I think of the Far Seer... Well with the DK and Lich, first you death coil their hero, then frost nova and repeat. If you hit enough, they should be dead, which gives a significant advantage to you.
So in short:
- try to avoid damage
- upgrade armor
- use corpses
- keep heroes behind battles
- upgrade 1st zig into nerubian
- start with DK/fiends/Lich/statues/destroyers strategy (in that order)
- coil/nova their heroes continuously