First off a STAX deck MUST have a low curve. A good prison deck should have a curve around 2.5 and the lower it is the better since a lot of these cards are causing prison effects on everyone's lands (Winter Orb, Static Orb, Tangle Wire). Having a low curve is vital because it allows a STAX deck to play in the playground of pain and taxation without being set back too much by the negative effects. Powerful ramp and land reanimation like Petrified Field, Lodestone Bauble, Groundskeeper, Gaea's Blessing, Life from the Loam, Loaming Shaman, Ramunap Excavator, Splendid Reclamation, and the Crucible of Worlds are great for STAX decks as well. Choosing the right form of ramp for your STAX deck is also important. For example, consider running mostly mana rocks like Sol Ring if your deck plans on using a Cursed Totem while mana-dorks like Birds of Paradise would be superior if you prefer things like Null Rod. Draw engines that can survive a STAX decks oppressive effects such as Vampiric Rites, Dark Tutelage, Dark Prophecy, Phyrexian Arena, or Necropotence are essential for maintaining tempo. The worst thing that can happen to STAX deck is for it to fizzle out midway through the match.
Since the curve of the deck should be low, most of the creatures in the deck shouldn't be very strong body wise. A STAX decks creature base should be filled with creatures that accelerate, defend, or are "Hate Bears" which help with your strategy. Equipment cards like Masterwork of Ingenuity, Blade of the Bloodchief, Bloodforged Battle-Axe, Blade of Selves, Sword of the Animist, Nim Deathmantle, Umezawa's Jitte, Sword of Fire and Ice, Sword of Light and Shadow, Sword of Feast and Famine, Sword of War and Peace, Loxodon Warhammer, Behemoth Sledge, Fireshrieker, Bludgeon Brawl, Grip of Phyresis, Sunforger, Grafted Wargear, Grafted Exoskeleton, Deathrender, Hammer of Nazahn, Assault Suit, and Batterskull are great in STAX decks since they allow the weak "Hate Bears" (Grand Abolisher for example) and Reassembling Skeleton variants to actually have a chance at trading with something bulky. Having a reliable finisher whether it be a plethora of ridiculous equipment or a powerful combo is important to eventually close out the game and end the opponent's suffering. Forcing scoops is another way to win if your deck is built to completely lock other players out of the game but this strategy "should" only be employed by chaos decks where their only other win condition is a unreliable slap from Norin the Wary.
Once a strategy has been chosen, utility cards must be added so that the STAX deck can recuperate faster than the opponents. This is done by fielding strong reanimation like Mimic Vat, Yawgmoth's Will, Magus of the Will, Hell's Caretaker, Whisper, Blood Litergist, and Living Death to name a few or degenerate self-reanimating creatures like Gravecrawler, Dread Wanderer, Tenacious Dead, Reassembling Skeleton, Bloodghast, Nether Traitor, Nether Shadow, Nether Spirit, Brood of Cockroaches, Endless Cockroaches, Mortus Strider, Squee, Goblin Nabob, Squee, the Immortal, Vengevine, Phytotitan and Advanced Stitchwing. Another strategy is to abuse creature tokens (think of Bitterblossom, Zombie Infestation, Nest of Scarabs, Sengir Autocrat, Endrek Sahr, Master Breeder, Grave Titan, Army of the Damned, Secure the Wastes, Martial Coup, White Sun's Zenith, Elspeth, Knight-Errant, Anointed Procession, Spirit Bonds, Luminarch Ascension, Dragonmaster Outcast, Daretti, Ingenious Iconoclast, Goblin Assault, Krenko, Mob Boss, Siege-Gang Commander, Awakening Zone, From Beyond, Creakwood Liege, Nath of the Gilt-Leaf, Mycoloth, and Avenger of Zendikar) or base the deck around non-creature spells like enchantments (Hanna, Ship's Navigator), artifacts (Daretti, Scrap Savant), and even planes-walkers (Atraxa, Praetors' Voice).
When building a STAX deck it is important to commit to a specific strategy and to choose colors that support that strategy. Each color in Magic the Gathering has its own strengths and weaknesses which are important to keep in mind when building a deck.
: Sacrifice and Destruction Effects, Hand and Board Disruption, Discard, Creature Reanimation, Life for Cards, but cannot deal with Artifacts and Enchantments.
: Exile and Destruction Effects, Mass Land Destruction, Taxation, Defensive Life Gain, Permanent Reanimation, but does not draw large amounts of cards and has a hard time mounting comebacks.
: Massive Mana Ramp, Amazing Creatures, Strong Non-Creature Permanent Removal, Card Advantage Engines, but lacks creature removal and struggles against continuous board wipes.
: Massive Card Draw, Counter-Magic, Taxation, Mind Control, Artifact Support, but lacks good blockers and hard forms of removal.
: Combat Mastery, Chaos Effects, Mass Land Destruction, Mind Control, Artifact Support, Hardcore Burn, but lacks card draw and cannot deal with Enchantments.