There is a lot to talk about here, so may as well get started. The main focus of the deck is, obviously, resolving Birthing Pod. Thanks to Green Sun's Zenth and its ability to grab Dryad Arbor, as well as the inclusion of Birds of Paradise, this can be done as early as turn two. Another great potential turn one play is Veteran Explorer, who is absolutely amazing with Pod and Cabal Therapy. The mana ramp he provides is just great to have in general, considering the deck has such a high mana curve.

From the moment Pod resolves, you will find yourself with a plethora of decision trees. Which creature you Pod for and which chain you follow all depend on the deck you are facing and the situation at hand. Practice makes perfect: knowing the deck and the purpose of each inclusion is key. Podding off of Dryad Arbor can net you an Explorer or Birds for additional mana ramp or color fixing. Sacrificing one of these dorks gives you the choice of Strangleroot Geist, Viridian Emissary and Wall of Blossoms. Geist is your aggressive option, and works amazingly with Pod thanks to his Undying. Wall of Blossoms is your defensive option, which also nets you a card once it comes into play.
Finally, Emissary is a nice target if for any reason you think you need even more mana.

Your three drop slots are filled by Bone Shredder, who acts as a tutorable kill spell (just be careful of his echo cost, which cannot be ignored due to the sorcery speed activation of Pod), Glissa, the Traitor, who revives fallen Pods for you, and Eternal Witness, who can do the same, but also grabs anything else you may want a repeat showing of.

The four drop creatures are where the fun really begins. Entomber Exarch starts the real card advantage going, either decreasing your opponent's choices or increasing yours. Skinrender is a nifty removal option that can get rid of a whole selection of creatures, and make the larger creatures much less threatening. Solemn Simulacrum finds you lands (as if you hadn't been doing enough of that already) and draws you cards. He is a nice vanilla option when you don't necessarily need a bullet at the time. Finally, Wickerbough Elder helps get rid of artifacts and enchantments that may be causing issues.

Acidic Slime is probably the most famous and versatile of your choices. As five drop slots go, he can't be ignored. The Slime can act as an additional Wickerbough Elder, an aggro deterrent with his deathtouch, or a Stone Rain for nasty lands like Maze of Ith and Karakas. Vorapede is another aggressive Undying pick. The board advantage that he provides is awesome, and the creatures that follow him are even better.

Brutalizer Exarch is your six drop silver bullet. He answers just about everything short of a beat stick, and can find you any creature in your deck. This helps if your chain gets broken, you want to start a new one, or you just need a specific bullet and Pod can't quite find it for you. Grave Titan is your main finisher, and man does he perform. I mean, he is literally a giant zombie that sweats out more zombies. Keep in mind his Zombies can be used with Pod. I'm not sure when that situation might ever arise, but you never know. Last of the six drops is Massacre Wurm, your mass removal that can also act as a sort-of reach card. That's not to say that he can't beat face when the time comes though... because he totally can.

Your final link in the chain is Sheoldred, Whispering One, and boy is she a doozy. Bringing back every creature that you ever used to Pod is awesome. Getting rid of every creature your opponent owns at the same time is even more awesome. This board wiping happens even faster when you repeat the use of all of your removal bullets over and over again. Bring them back, kill something, sacrifice them to pod and repeat next turn. Your opponent will spend the rest of the game without a creature — not that the rest of the game will last must longer after this.

Sideboard Suggestions-
Combo is a problem for you, as it takes a long time for a deck like this to get going. Discard spells like Duress and friends are nice for this, while also coming in against other random decks. In a deck with so many mana sources and creature spells, Thorn of Amethyst is also viable. Heck, Mindbreak Trap isn't even too crazy depending on your meta. As far as graveyard based combo goes, Scavenging Ooze is pretty expensive, but Withered Wretch can still be found via Pod. There is also the traditional Tormod's Crypt and friends (which can be re-used thanks to Glissa).

Control is your strong area, so not much is going to come in against them. Really, you just attrition them out of the game. Specific bullets could be used, and cards like Krosan Grip, Beast Within, or Abrupt Decay would be fine as well.

Against aggro you have the benefit of running black, which means you have a plethora of removal spells at your disposal. I like Smother, but there are a ton of options out there, so go to town. Also, cards like Engineered Plague wouldn't be too out there to play either, and can really help against those swarm happy tribal decks.