This is an example of a budget Modern deck that can be modified as necessary for an expected metagame.
How it works:
1) Keep a hand with mana and spells.
2) ????
3) Win on turn 20 or so.
It is just about that simple. Simply kill off any significant creature threat that your opponent fields against you, and counter any noncreature nasties like planeswalkers and Sphinx's Revelation with your counter package of Rune Snag and Rewind.
The main thing to get used to is playing on your opponent's turn. There are very few situations that you should ever need to play something on your own turn, which you should learn naturally as you play the deck. In most situations, it is better to wait until the end of your opponent's turn to cast Mystical Teachings to find an answer or a Rewind.
Explanation of card choices:
Calciform Pools/Dreadship Reef: Often, at the end of an opponent's turn, you may have some extra mana. One option is to spend 2 here to store up some mana for when you really need the excess. These are known as "storage lands."
Careful Consideration: Helps filter out your draws in the mid- or late-game when you can discard cards that are useless in the matchup (removal against control, etc.) or excess lands.
Consume the Meek: While expensive, it is instant speed, which means it is tutorable with Mystical Teachings. It is decent against tokens and aggressive zoo builds.
Creeping Tar Pit: The primary win condition for the deck. Protecting these or swinging while the opponent is tapped out is best. They are unblockable, but they can also block small creatures if necessary.
Darkslick Shores and Seachrome Coast: Cheap dual lands that allow you to have open mana for counters and removal spells in the early game. Entering tapped in the late game is not that bad because efficient use of mana should have left some counters on the storage lands.
Desert: Very efficiently deals with X/1 creatures by only giving them one attack step. Kills Snapcaster Mage, unflipped Delver of Secrets, Dark Confidant, Lingering Souls tokens, mana elves, and more.
Devour Flesh: kills Geist of Saint Traft at very little cost. Probably one of the best edict effects in modern at the moment. Lifegain isn't an issue because we play for the long game.
Disfigure: A very good turn 1 removal spell for Goblin Guide, but it kills Snapcaster Mage, Dark Confidant, and other little guys. Works wonders against Affinity.
Dismember: Good for targeting combo creatures for a cheap cost. Paying four life is an option, but the mana base can usually support the double black requirement on turn 3 if necessary.
Go for the Throat: Kills Tarmogoyf. Good enough for me. Be sure to side it out against Affinity.
Grave Titan: A secondary win condition that puts 10 power and 10 toughness on the field over three bodies. Very difficult to deal with outside of a counterspell. Casting it on turn 6 can be good against midrange decks like Jund, but this is actually tutorable with Mystical Teachings after getting Teferi, Mage of Zhalfir on the field. Makes for a very good EOT tutor and main phase threat.
Mystical Teachings: This card is the sole reason that control is playable in the Pauper format. That's right, this card is a common. It is also one of the few tutors in Modern. Unlike other tutors, it also has flashback. This card is just amazing. It fetches wrath effects, removal spells, counterspells, threats, and then does it again with flashback if necessary. When you have some of these stranded in hand they make good cards to draw out counterspells because of the flashback and also can search out Rewind for whatever your opponent plays next. What's more, you can cast one of these after a Rewind to take advantage of the untap effect.
Path to Exile: The second best one mana white removal spell in the game, after Swords to Plowshares. Use these only on ridiculous threats like Titans, big Tarmogoyfs, and combo creatures or value creatures like Kitchen Finks or Murderous Redcap.
Pulse of the Fields: Really shores up your aggro matchup by repeatedly gaining you life until you have enough mana to wrath. Eventually helps win against straight burn decks because they run out of damage and start playing off the top, 2-3 damage at a time. If aggro is more dominant in your meta, you can also consider Death's Shadow.
Rewind: Counters anything scary, but is a little expensive. However, the untap effect allows you to cast Mystical Teachings right after it, to search for an answer or another Rewind.
Rune Snag: Starts out worse than Mana Leak, but it gets really great. Let your opponent try paying 4-8 extra mana for their spell.
Smother: Kills most scary threats in the format.
Spell Pierce: This card is made to counter Liliana of the Veil. Our biggest enemy and vulnerability is an uncountered Liliana. How convenient. We are happy playing 2.
Surgical Extraction: Stops reanimation shenanigans from TinFins, kills Living End value decks, and is good any time for only 2 life. You can also consider Extirpate if you find some good targets for it in your meta.
Teferi, Mage of Zhalfir: Shuts down combat tricks, EOT effects, and counterspells from your opponent until they kill it through your countermagic, which is pretty tough. Also allows Grave Titan to be tutored with Mystical Teachings.
Think Twice: Makes a great draw engine due to flashback, and gives you something to do with that extra bit of mana you have left at the end of their turn. Also helps you hit your land drops if you use it main phase.
White Sun's Zenith: Another secondary win condition that can be hilarious. No one likes being scratched to death by cats. This can be awesome as early as turn 6 if you get a storage land down and activated early enough. However, you do need to watch out for counterspells. Leave open mana for a counterspell if you have one, and leave it open anyway to scare your opponent into not countering it. You never know. Sometimes they "misunderestimate" (-George Bush) the card. Don't expect to be able to cast it twice, but it can make a great teachings target late game if your opponent is tapped out.
Sideboard:
Pithing Needle comes in against Liliana of the Veil. That is actually one of the only things that outright kills this deck.
Day of Judgment, an extra Consume the Meek, Darkblast, and Timely Reinforcements come in against aggressive decks.
Celestial Purge is for Jund.
Dispel, Detention Sphere for UWR control/Gifts control/the mirror.
Detention Sphere for help vs tokens, but its not that popular.
Purify the Grave for vs. TinFins/Reanimator/Gifts Control
