The core of this deck is in the synergy between Training Grounds, Pack Rat and Asylum Visitor. How this works is that Training Grounds + Pack Rat let's you dump your hand super fast to make huge swarm of huge rats, discarding Asylum Visitor into play with madness which in turn refills your hand.
The rest of the deck is a supportive control package and more synergy with training grounds and discarding/filling your grave.
The game plan is usually more tempo than aggro oriented, so for example Training Grounds - Remand/Mana Leak - Pack Rat + discard(dodges removal) is a more suitable and safe 3 turn opening than straight Training Grounds - Pack Rat - Tripple discard even if the latter sequance technically wins a turn faster unopposed. The typical finish is simply overwhelming with Packs Rats or tapping down blockers with Cryptic to enable a lethal attack with Pack Rats, but slowly grinding an opponent down with value advantage from Nezumi/Tasigur/Snapcaster while countering their threats works fine as well.
Nezumi Graverobber + Training Grounds lets you hate out the opponents graveyard quickly and once flipped can be used to steal their dead creatures or bring back your own for reduced cost. Incredibly good with Snapcaster Mage, for example bring him back over and over for chump blocking and extra spells. A flipped Nezumi benefits greatly from having 2 Training Grounds in play, playing any creature from any graveyard at instant speed for 1 black mana rather crazy and a very fun way to beat dredge and reanimator decks. Note that other than sometimes playing the extra copy for the flipped Nezumi, redundant grounds are better kept in hand for discarding to Rats or Brutality.
Tasigur, the Golden Fang comes out cheap with delve and is great card advantage engine with Training Grounds out.
I won't go over the staple counterspells, hand disruption, card selection and removal package in detail. It's the usual kind of stuff in the proportions I thought works best for the deck. This can be adjusted rather freely as long as there is enough instants and sorceries justify the snapcasters. I opted for Serum Visions, Fatal Push, Inquisition of Kozilek, Collective Brutality, Remand and Mana Leak. Other good options to consider are things like Thoughtseize, Hero's Downfall, Spell Snare and so on.
Just the Wind may seem odd since it's not a very strong card in itself, but it has great synergy with Pack Rat and Snapcaster Mage. You can for example make a rat discarding the winds into play with madness to bounce the mage, or EOT discard winds to rat to bounce an enemy blocker while getting lethal board. It's been great in testing so far.
Snapcaster Mage Slots perfectly into the deck, not only is it perfectly competitive on it's own in any blue spell heavy deck, but we also have ways to bounce him or bring him back from the grave for recurring value in grindy games.
Cryptic Command is just an awesome card to solve tricky positions, but one of the main applications here is to tap down a wide enemy board state so your rats can swing for lethal.
Creeping Tar Pit If you get locked in a clustered board and can't attack with normal creatures, if you're on the grindy control plan and need a clock, if your attack needs 1-3 extra damage to be lethal, or if you simply have nothing else to do due to mana flooding or whatnot.
That's basically the deck, on to sideboard. Obviously this is expected to be adjusted for the given metagame.
2x Big Game Hunter - Has good synergy with Pack Rat and is boarded in against creatures too big for Fatal Push
1x Ceremonious Rejection - Against artifact decks and Tron.
1x Collective Brutality - Second Copy mainly against Burn.
2x Echoing Truth - Against tokens and adding bounce to deal with enchantments and such.
2x Hurkyl's Recall - Against Affinity, Lantern and other artifact decks.
1x Negate - Harder counter power against control and combo.
1x Notion Thief - Against card draw heavy decks to negate their advantage, also beats some combos.
3x Relic of Progenitus - GY hate, but can also be good against creature heavy decks to help flip Nezumi to steal their creatures.
1x Spreading Seas - Mainly vs Tron.
1x Tribute to Hunger - To get around protection, hexproof and indestructible.