UB can sometimes also be built as a control deck where you eliminate your opponent's threats until you can drop your own and win, but I'll focus on the milling aspect of the two colours for this deck.
The following are the cards you want to look for and draft
- Thought Scour
- Mind Sculpt
- Dream Twist
- Psychic Spiral
- Nephalia Drownyard
- Selhoff Occultist
- Vedalken Entrancer
- Belltower Sphinx
- Undercity Informer
- Oona, Queen of the Fae
- Psychic Strike
- Coerced Confession
- Pilfered Plans
- Codex Shredder
These are the main milling cards in the cube and if you can grab a few of them (especially the recurring ones) you can easily mill your opponent out as the decks are usually only 40 cards (And of those 40 cards you only need to mill away around 30 or so).
In addition to the actual milling cards it helps to pick up some defensive creatures like Wall of Frost, Fog Bank and Mnemonic Wall so you can stall your opponent. Some kill cards like Doom Blade or Murder are also useful for taking care of things your walls can't stop.
There are a few cards that may not seem like they would fit but are actually really good for the deck. Jace's Archivist and Prosperity can help you achieve your goal of milling your opponent. Jace's Archivist may not seem useful but if you are milling your opponent they most likely will not have as many lands as you so their hand will be fairly large. The added cards will usually be more beneficial to you than it will be to your opponent. Similarly Prosperity can force your opponent to draw more cards than he intended and bring him closer to being milled while at the same time filling your hand with more useful spells.
Of course if you can't mill your opponent to death, you do have the option to go on the beatdown, especially if you can land a few large creatures like Oona, Queen of the Fae, Frost Titan or Lazav, Dimir Mastermind. If you've milled your opponent early enough it will be easier to drop one of these bombs and just take over the game. This alternate strategy is also advisable after game 1 where your opponent might side in more cards to make his deck bigger and harder to mill so for your own sideboard you might want to add some unblockable creatures like Keymaster Rogue and Deathcult Rogue to your sideboard and switch strategies between games. These creatures also work well if Trepanation Blade is already in your card pool.
Like the other decks I looked at it is a fun deck to play, especially if you like frustrating your opponents.