Alright, you've learned a lot of the ins and outs of the deck list, now its time to learn how to play the deck.
This deck averages a four turn game, so keep that in mind when I use terms like "early game, mid game, and late game." Early would be turns 1-2, three at the latest. Mid would be 2-3, and late would be 3-6.
From the get go, you want to be putting in accelerants and possibly refilling card advantage (believe me, I can drop my hand easily on turn one, its often very relevant to be able to refill as well). Mana Crypt is a relatively common turn one play from this deck. Naturally drawing it feels great as always, but its also a very good turn one Demonic Tutor option. The best plausible turn one involves making a few extra mana, then casting a Windfall effect. If you go first and do this you probably win the game straight off. There are ways of entwining Tooth and Nail on turn one with enough lands and a wincon, but they're astronomically unlikely and shouldn't be expected.
Turn two should be spent playing more acceleration and either a tutor or a redundancy piece. Depending on your start, you might be casting Damia or Tooth and Nail on this turn. If you're casting Tooth and Nail, make sure you actually have the resources and capability of winning on the spot. If not, save it and just play Damia. A Damia play on this turn is extremely safe. Most of the time, people are trying to set up their own boards and don't want to have to remove her (or they just can't). If you untap with a turn 2 Damia, you're going to win, quite possibly on the spot. Even if they remove her, you still ate some removal or counterspells, and the real wincons are more likely to resolve as a result. More realistically, you're going to be playing more acceleration and a wheel. This is also a super common Ad Nauseam turn. If you cast it and resolve it, you can feel pretty safe going to very low life totals. I generally drop about 25-30 life into Ad Nauseam.
Here, I would like to further reinforce that solving all the board's problems is not your job. You just can't do it and expect to win in a timely manner. Just because somebody else got a good start doesn't mean you should start holding up counterspell or removal mana. Focus on getting your own start unless its absolutely necessary.
Turn three is the first turn you can reliably start winning the game. If turns one and two went average, turn three can be spent playing Damia or redundancy. If you still need a bit to close the gap to 9 mana, play another accelererant. Otherwise, feel free to tutor for (or just cast) Tooth and Nail / Time Stretch. A big Stroke of Genius or USZ is good here. If Ad Nauseam resolved at the end of the second turn, you're (very) probably winning upon untapping. Don't even bother trying to hold a counterspell to protect Tooth and Nail. If an opponent had a response to a spell, they would have stopped Ad Nauseam. The only thing to be wary of is removal. If the coast is clear, go for it.
Turns four and on are simple. Just keep jamming wincons until one sticks. If the game goes too long, you might want to actually begin holding some answers to the wincons of your opponents.
Now, I'd like to examine some sample hands. These were randomly generated, and I just picked the first three keepable hands.
Our first hand (after one mulligan, six lands and a ritual) is Riptide Lab, Bloodstained Mire, Forbidden Orchard, Strip Mine, Snap, Yawgmoth's Will and Chrome Mox. Its heavy on lands, but that reduces the likelihood of drawing them later when we're looking for substance. Honestly, this is one of the worst hands possible, but its got acceleration. I would definitely keep this over going to six, but if you still have your free mulligan, take it. Anyways, since I used my mulligan, I'll keep. I'm instantly rewarded with the top card of the library being Intuition. The best play here is to just crack a Mire and further reduce the number of lands in the deck. Now I have no idea what the next card you draw into will be, but if its a land or a card more relevant than Snap, exile Snap to Chrome Mox and play a land. You probably don't care about anything quite as much as resolving an end of turn Intuition. You probably want to find Crypt, Sol Ring and Mana Vault here. Turn three will be spend casting Yawgmoth's will, getting back all of the mana rocks and Intuition. If you play your cards right, you will win on turn 4.
Our next hand comes immediately after the last. No mulligan was required. This time we have Exotic Orchard, Reflecting Pool, and Crystal Vein for lands. We have Simic Signet, Lotus Petal, Brainstorm and Lim-Dul's Vault. This is a super keepable hand, even with no lands that produce colored mana on turn one. Our first draw is Breeding Pool. Very useful. Unfortunately, this hand is very open and a very large number of lines of play can happen, depending on the piles we see with Lim-Dul's Vault. I would spend turn 1 playing Petal and Breeding Pool, then resolving an end of turn Vault. With Brainstorm, everything is much more powerful. We'll be able to see four of the five cards we set on top. Without more information, I would predict this hand to win on turn four. Turn three is possible if the Vault pile is very good. If the pile is average, turn five would be the latest I could expect.
Our third hand comes immediately after the last, requiring no mulligan. We rolled really well this time. We have Overgrown Tomb as our only land in hand. We have Mana Vault and Crypt, along with Mystical Tutor, Intuition, Gilded Drake and Yawgmoth's Will. This is a snap keep if I've ever seen one, even if there is no blue mana. Our top card is Felwar Stone, and everything is beautiful. We're a bit slower if we go first, but if even one player goes before us, we explode. Turn one (assuming we aren't first, as its more likely) should be spent playing Crypt, Fellwar Stone and Mana Vault. You can play your Tomb tapped to save some life. Turn two will be started at 7 mana. Depending on our draw, we can either play Damia or just go with plan A and use Intuition and Yawgmoth's will in a similar fashion to our first hand. I would expect this hand to win on turn three. Four if somebody stops us.
Since that last hand was really cheesy, I decided to roll one more hand. The lands are City of Brass and Cephalid Coliseum. The fact that both of these deal damage to tap is troubling, but the rest of the hand is worth it. We have Sol Ring, Green Sun's, Scroll Rack, Snapcaster Mage and Noxious Revival. This is a snap keep. Our top card is Swan Song. Lame. We have two lines of play. Turn one we can play City, Sol Ring and Scroll Rack. However, I think it would be more beneficial to go ahead and GSZ for Dryad Arbor and call it a turn. We do this because Dryad Arbor has summoning sickness, and also because we NEED to get to three lands that don't damage us to combo off. On turn two, hold off on playing the Coliseum. We possibly need to drop Sol Ring and Scroll Rack, so we can dig for a land that doesn't hurt. As everything at this point relies on what we see with the Rack, I'll just hall my prediction that this hand would most likely score a win on turn four or five.
This is rather fun, so I'll roll one more hand. No mulligan required again. We have Urborg and Windswept for lands. We also have Chrome Mox, Demonic Tutor, Lim-Dul's Vault, Noxious Revival and Cyclonic Rift. This isn't quite Magic Christmasland, but its close. Our top card is Toxic Deluge. We ended up with half our removal suite in our hand. Windswept for Breeding Pool and Chrome Mox exiling Deluge allows us to tutor for Crypt. We can then cast Noxious Revival on our upkeep to get the Tutor back. We can tutor for Sol Ring and play it with mana from Crypt and Chrome Mox. We still have Urborg and Breeding Pool up, so we can cast and end of turn Vault. Remember, we have Rift, so a real option is holding back and Rifting end of turn, then casting Windfall. Another good option is casting Damia. The Vault can be used however it needs to be with the board state. I personally like the Windfall plan, but if you can get a good set of cards together, you might just be able to win on turn three. So I'd predict this hand to win on turn 3-5 depending on the line of play you choose. If you go with Rift, you probably win on turn 4-5.