Lets start by looking at her measurements, I mean stats.
First, she has a CMC of 3, best you can get for a planeswalker.
The two black requirement means that you have to have a commitment to black, but since the CMC is only 3 you could have some form of mana conversion (something that changes one color of mana to another) and still get her into play relatively early.
Some people have talked about her as being similar to Jace Beleren. Lets see how they stack up.
Both have a CMC of 3 with a requirement of two of the same color. The casting cost is equivalent.
Both have three abilities.
The first ability for both has to do with cards and options. Jace gives each player one more card while Liliana takes a card away from each player.
The second ability for each card gives advantage to one player. Jace gives one player another card while Liliana takes a creature away from a player.
The third ability, the ultimate, for each is something quite different. Lilianna makes a player choose losing up to half of their permanents. Jace mills for twenty.
On the surface it may seem that the two walkers are very similar. The plus ability gives options or takes them away. The second ability gives advantage to one player. The ultimate can hurt, but not obliterate an opponent. You could argue that they cards are quite similar in power level. Some ways of looking at the match-up might suggest that they are similar in power level. Context, however, is king, and Liliana is more rocking than she seems prima facie.
The First Ability: Give and Take
Jace Beleren's first ability is +2 and each player draws a card. Nice! You get an extra card on your turn and since you are playing blue, counter magic is probably in the deck somewhere. Your opponent gets an extra card, but you have priority and its your turn, its at worst a minor drawback.
Liliana of the Veil's first ability is a +1 and each player discards a card. Oh, that stinks. Your opponent has to discard a card, that is nice. But you have to discard a card as well. Major drawback right. Unless you unload your hand first. So you could unload burn or creatures before you start using Liliana's +1 to keep your opponent out of options.
But wait, this is where context is king. Flashback is a major theme in Innistrad. Discarding can be a benefit. Some cards have a flashback cost that is less than the original CMC. Unburial Rights is the first card that comes to mind. CMC of 5 but a flashback cost of 4. So a turn three Liliana of the Veil can hurt your opponent by making him ditch a card and can allow you to drop the Grave Titan into your graveyard. The next turn you can +1 again and drop an Unburial Rights while further limiting your opponent and then flashback a creature into play. Usually a creature that you could not have put into play otherwise.What seems like a very similar ability actually is a huge advantage engine given the context of flashback and cards like Unburial Rights. Jace's +2 gives you marginal advantage, not in cards but in play options, since you get the card on your turn and at your discretion. But still you are drawing a card and most of the time you won't know what that card is. Your opponent also gets another card which gives them more options also.
Liliana's is much different. Instead of giving both players more options by drawing a card, both players discard a card. Options are reduced. Except that the graveyard mechanics of Innistrad allow for discarding cards to be a form of card advantage. So forcing an opponent to discard can be a huge advantage for you and discarding a card that you need in your graveyard can be a huge advantage for you also. Stand alone Liliana of the Veil can help to suffocate an opponent, given Innistrad she can also strengthen you at the same time.
Liliana of the Veil is superior to Jace Beleren, and given Innistrad, clearly superior.
The Second Ability: Pure Advantage
Jace Beleren's second ability is -1 target paler draws a card. Simply card advantage, love it. Liliana of the Veil's second ability is -2 target player sacrifices a creature. She can protect herself. A planeswalker that can help keep creatures at bay. Since you are playing black you also have access to plenty of spot removal. Since Liliana does not target a creature protection from black, hexproof, shroud, and anything else that would protect a creature from being targeted does not apply. Of course she can't be specific about which creature gets sacrificed, but with spot removal available, the choices can be narrowed.
Liliana's ability is better early in the game and Jace's ability is great any time. Being able to remove creatures from the board is nice. This is what helped propel JTMS to stardom. JTMS only bounced them and Liliana sends them to the graveyard, but then JTMS was only -1 and Liliana's is a -2.
This ability can be awesome for Liliana, but against non-creature decks it is useless. Jace Beleren's ability is always useful so while Liliana's ability is much more powerful, it is also much more contextualized. Jace's is good regardless.
Liliana gets the nod on the second ability also, but sometimes it may just be useless.
The Ultimate: Game Changer not Game Ender
Jace Beleren's ultimate is -10 mill target player for 20. Liliana of the Veil's ultimate is separate target players permanents into two piles they get to keep one and sacrifice the other. Lets be honest, you can win the game by milling an opponent. Jace Beleren's ultimate given the right circumstances can win the game. If a game grinds to a halt and Jace is on the board ready to pop the ultimate the clock is shortened and unless you are a mill deck, you have an alternate win condition. If you are playing a mill deck, then his ultimate is the same win condition you already have built in. In most games, however, milling for 20 on turn 6 is not all that exciting. Liliana's ultimate will give you board advantage, but it might not simply hand the game to you. Still losing half of your permanents can be devastating, it just might not be all that bad.
Liliana's ability is better in most cases but it is nothing to write home about.
Going on from here
Liliana of the Veil is clearly better than Jace Beleren. Her best attribute is her +1, but the -2 is awesome given the right situations. Her ultimate is ok, but if you are going to use her plan on utilizing the first two abilities to get massive advantage so that you can put the game away.
What are the ways you can use Liliana of the Veil. Given the current context I think a Black & White for Unburial Rights is the best option. Ditching fatties to unbury is the best use at the moment. The Black, White, and Blue "Solar Flare" types have best options that I can see. You could go heavy black with white splash for the flashback but you will need to have early white mana so the mana base will have to include enough white to make it work. Or you could play white and splash black with some mana conversion to get the two black needed for Liliana.
If you want to ignore the flashback of Unburial Rights, you could go Black & Red for quick burn so the dumping of cards doesn't hurt as much. Or Black & Blue with think twice and other card draw to help you out overcome the discard letting Liliana take care of the creatures for you.
