I'm going to assume you want to play traditional Dredge because transformational Dredge is a lot more expensive.
Required pieces:
4 Bazaar of Baghdad
4 Serum Powder
4 Golgari Grave-Troll
4 Stinkweed Imp
1-4 Golgari Thug
4 Bridge from Below
4 Cabal Therapy
4 Narcomoeba
3-4 Bloodghast
1-2 Dakmor Salvage
7-8 Rainbow lands (Undiscovered Paradise, Mana Confluence, City of Brass)
There's other cards that you may choose to add, such as Riftstone Portal (as a 1-of), Library of Alexandria, and Petrified Field. Petrified Field is excellent Wasteland protection and you should fit as many as you can into your deck. My current build only has two because Shops is so down recently, but if I were to face a lot more Wastelands, then I would go to 3 or 4.
Build dependent:
2-4 Ichorid
2-3 Dread Return
1 Dragonlord Kolaghan OR Flame-Kin Zealot
0-3 Sun Titan
0-3 Fatestitcher
0-1 other DR target (optional; you can have main deck Elesh Norn or Ashen Rider for toolbox options, if you wish)
*note about build dependent section: Generally you choose how heavily you want to invest in combo. Heavy combo versions might have only 2 Ichorid, or sometimes even less, and sacrifice some other slots for cards like Sun Titan and Fatestitcher for speed; less heavy combo versions might have 3-4 Ichorid and only 2 Dread Return and DK or FKZ, and possibly one more toolbox Dredger. Less combo versions make more room for disruption cards.
Disruption package:
4-8 Disruption cards (Leyline of the Void, Unmask, Mental Misstep, other)
Remember you're still using 4 Cabal Therapy no matter what
Sideboard:
Dedicated to anti-hate cards. You want to be able to answer opposing Artifacts, Enchantments, and Creatures. Common selections include Nature's Claim, Ingot Chewer, Wispmare, Serenity, Barbarian Ring, Cabal Pit; there's many other options out there. Using Serenity, Ingot Chewer, and Wispmare instead of Nature's Claim allows you to dodge opposing Mental Missteps, which is very useful. I know Mr. Brophy advocates skipping Nature's Claim. Note that you could choose to transform instead of fight their hate, but such a build is more expensive, hence my assumption that you're going to fight their hate.
If you're interested in budget, you may want to use City of Brass over Undiscovered Paradise, as that can save you almost 100 dollars. Also, Unmask and Serenity are very expensive, if that tips your decision.