Annoy your friends or enemies. Counter everything in your path. If they cast it, then unsummon it and counter it like you should have. Not many creatures in this deck, so the secret is to let nothing through.
All of the counters should be based on the situation presented. For example, if somebody casts an Instant on your creature and you have a Turn Aside, use it instead of the Cancel. If a card used up all of their mana to cast, use Mana Leak or Spell Pierce, or if you have the mana, use the more expensive Summoner's Bane or Lay Bare or the kicker cost of Into the Roil. Use only the more generic Cancels when you have no other choice.
Winning the mana game is important, especially early game. Even when faced with a land heavy deck, you should still be even or better at the mana game, since most of the big mana decks require those spells that they can't cast to get all of that mana. Eventually, you will be spending less mana than your opponent, as he will want to get the 5-8 mana big creatures out, and you will deny it with 1-3 mana cards.
Creatures are rare in this deck, so treat them like gold. Don't put out a creature unless you have the means to counter other spells that may destroy it (or at least an Unsummon or similar to bring it back, but that is wasteful in mana cost). Remember, you're going to be in it for the long haul, and you're in control here. If you've done your job, there isn't much on his side, anyway. Also, be careful with leveling up creatures when you may need the mana for countering.
Enclave Cryptologist is one of the main card drawers, so that you have the choices required to counter any card type. When she is at level 1-2, it does a discard, so only use it if you need to counter a spell and you don't have the appropriate spell to use (as it is an instant ability). Surrakar Spellblade is the other card drawer, which works off of your constant countering. Only downside is that you have to make sure your opponent is defenseless, as you don't want him to die. Archmage Ascension works with both of them, and will eventually allow you to search for the right counter every time.
The Lullmage Mentor will eventually make your job easier, as his army of Merfolk will counter for you. (You can use the extra ones to attack the enemy.) The Echo Mage will either multiply your own counters (when faced with counter/instant war), multiply your unsummons (if several creatures already stomped through), or just create havok by using their own high-end spells against them (while your countering the original spell).
The main weakness in this deck is small creature or small mana decks, as they are better at the mana game than you. The sideboard provides several cheaper cards for countering these decks. Dispel is good for burn decks or ones with a lot of instants. Flashfreeze works as a better replacement for Cancel when faced with G/R decks. Whiplash Trap is great against cheap creature or token decks, exiling tokens and bouncing creatures back into their hand. Halt Order is good for killing off Eldrazi bosses or other artifact decks.