You'll have to think a few steps ahead of the Undead player during this battle. Here's a few do's and don'ts that should get you started.
DO scout. The Undead player's gonna be doing the same to you, so go right on ahead and do it to him. Keep in mind he has a scouting advantage over you, and always assume he is a step ahead of you. That usually spurs you on to think faster.
DO kill his heroes. His heroes are the backbone of his army, perhaps moreso than any other race in the game, because they are so powerful in comparison to their units. If you can seize an opportunity to destroy one, take it.
DON't kill his heroes blindly. Going straight after a hero can have dire consequences. Though fragile, the Undead heroes are capable of lasting a very long time, as Coil has a mere 5 second cooldown and the user of Coil has the only spell in the game that directly heals the hero himself in Death Pact. Be smart. Going straight for the DK might not always be the wisest course of action.
DO build 1-2 towers at the beginning. Undead harassment can become one huge headache, and will likely interrupt you constantly as you tech. A Lich/Ghoul rush followed up by a Lich/DK/Ghoul follow-up can put you out of the game if you're not careful (proven).
DON'T build too many casters. Massing casters will only mean pain for you. Undead players have known how to counter them since 1.05, and you'll be screwed if you get too many. A max of 12 casters combined should be more than enough.
DO use your heroes. Your heroes can help you counter the Undead ones with... well, no, not ease. But a stunned DK is a lot easier to kill than a DK who's running around with Unholy Aura and Pacting when he gets a little too hurt.
DO creep. The Undead may be the game's best creeping race, but that certainly doesn't stop you from doing your own creeping. Remember that a Human Triple Hero (the game's 2nd strongest Triple Hero, after the Undead) is worthless if their combined hero level is significantly lower than two Undead heroes.
DON'T get careless with your heroes. The Undead will almost certainly abuse his hero killing potential to its maximum, and their abilities at hero killing needs no introduction. Divine Shield and Holy Light will have to be used religiously to keep your heroes in the battle, not to mention attacking your own heroes sometimes if they get hit by Sleep.
DON'T build too many Footmen. Just enough to creep effectively is good. Whether the Undead player gets Ghouls or Fiends, he will tear you apart if you stick with Footies. Knights or Gryphons are good units to work towards.
DO watch out for his casters if he gets any. Yeah, he's an Undead, but that doesn't mean he doesn't have casters. Curse can be annoying if it's stuck on all your units. Keep an eye out for it, Dispel when there's too many. And pay attention to your heroes in case they try a sneaky Cripple. Cripple isn't very noticeable if you're too caught up in a chaotic battle, and can be used by Undead players. I know I would.
DO get the MK. The MK is the single best hero to take on the Undead with, even if he does get his ass kicked more. He'll be your primary hero counter for the most part, so get him first.
That's all I can think of right now. Good luck.