The idea of this deck is to make it very hard for your opponent to attack your sites, because their minions are constantly at risk of getting dragged/lured/teleported/flown onto sites that will kill them.

Sites

Sites and site placement are absolutely vital in this deck. Mulligan for your best kill-sites (The Void, Bottomless Pit, Old Mortimer's Den), Wuthering Heights and Crossroads. Generally, put your 'normal' sites in your back row (Aqueduct, Crossroads, Garden of Eden, Lighthouse, Observatory, Tintagel & Windmill). There are exceptions though: starting with a kill site in your back row and placing a Wuthering Heights in front of it works great as well.

The Void

Use Displace, Led Astray or Wuthering Heights to move a nearby or adjacent minion onto it. If they don't have Voidwalk, they die.
Position your Pudge Butcher or Nelly Longarms, so that The Void is between them and the enemy minion. Drag the minion into The Void.
If you position a Coy Nixie adjacent to The Void, you can lure a nearby enemy minion into it (if that would bring the minion a step closer to the Coy Nixie).
If you summon or move a Gibbous Nightgaunts onto The Void, you can use Swap to move an enemy minion from anywhere in the realm to The Void.

Bottomless Pit:

Everything that works for The Void, also works for Bottomless Pit, provided the enemy minion does not have Airborne. Swap is easier to use now, because Swan Maidens, Sky Barons and Gibbous Nightgaunts all have Airborne.

Old Mortimer's Den:

All of the above also works for Old Mortimer's Den, except for Swap, because you cannot move or summon any minions of your own onto it.

Be careful though! Your opponent can sacrifice a minion by moving it onto this site and then place their own site on the resulting Rubble. For that reason, the ideal placement of Old Mortimer's Den is in your back row, safely behind (or at least nearby) a Wuthering Heights or River Rapids. Move an enemy minion onto the Wuthering Heights/River Rapids and from there move it on to Mortimer's Den. Play Mortimer's Den again on the Rubble. Rinse. Repeat.

Thin Ice:

Also kills (drowns) enemy minions, but the timing is tricky. It happens at the end of your turn. Move an enemy minion onto it during your turn (using any of the methods already mentioned above) and then, if the minion has less than 5 power, summon or move your own minion on top of it. Preferably a minion with Submerge, which will stay alive.

Ideal scenario is playing a Coy Nixie on Thin Ice and immediately dragging a nearby enemy minion on top of it. Or having Nelly Longarms do the same with an even longer reach. Nelly's ability is subject to summoning sickness though, so that is harder to make it work. Abaddon Succubus can do it as well, but will drown herself if you don't move her away in time.

The Manor at Daperyll Hill

Another to lure enemy minions onto. Good site to place an Abaddon Succubus, because she can safely occupy it and deals 2 damage herself, effectively killing minions with 5 Power or less that she drags onto the site. You can't use the Manor early game though, because of the high air threshold needed.

Wuthering Heights

Has already been mentioned several times. This card is extremely good in this deck, because it expands the range within which you can grab your opponent's minions. It's hard for your opponent to find a safe place to put his minion if you're able to chain several forced movement effects after each other. A Coy Nixie or Abaddon Succubus on a Wuthering Heights already gives you two steps of forced movement without using any magic spells.

River Rapids

Similar to Wuthering Heights, but providing forced movement only to adjacent sites. A River Rapids next to a Wuthering Heights is a lot of fun.

Baba Yaga's Hut

Switching sites around can obviously be powerful in this deck. Note that Baba Yaga's Hut does not need to be empty itself, so you can use it to move either your opponent's or your own minions to another location. An immobile Pudge Butcher in your back row suddenly isn't that immobile anymore if you put him on Baba Yaga's Hut.

Innsmouth Dock

Another possible link in the forced movement chain.

Crossroads

Needed to find your kill-sites and Wuthering Heights/River Rapids.

Minions

Most minions have already been mentioned. Some others:

Kettletop Leprechaun

You need to dig for your best sites. Sometimes your Leprechaun will be stuck on your back row behind your own Bottomless Pit. Don't be afraid to walk him straight into the Pit if you need a new site.

Skeleton Mage

Cast an extra copy of your Blink/Displace/Led Astray/Teleport etc.

Overbearing Bailiff

Cheap protection for your Avatar on your back row.

Ruler of Thul

Sometimes your own minions can get a bit stuck behind your own barricade of kill-sites. Ruler of Thul allows you to just hop straight to your opponent's back row and start doing damage. Buffs your Bailiffs and Pudge Butchers, who will often be in your back row.

Gloam Toad

Big minion that functions the same way as a kill-site. Drag a minion to an adjacent square and let the Toad finish him off. The Toad is immobile, just like Pudge Butcher, but there are many ways in this deck to move them onto an opponent's site, where they can do a move-and-attack like any other minion. (Blink, Displace, Teleport, Swap, Nelly Longarms).

Lord of Lies/Lord of Greed/Sky Baron

Big minions with strong abilities. While it is fun toying with your opponent's minions, you still need to win the game by damaging your opponent. Sky Baron is especially fun when your opponent has Airborne minions and is sitting on your Bottomless Pit, attacking it and feeling smug.

Crawling Congregation

Another relatively big minion. Helps with hitting only enemy minions with your Pudge Butchers, as well as protecting your avatar from enemy projectiles.

Artifact/Magic

Key to the City

A great card for the mana it provides alone. On top of that, it allows you to put a Coy Nixie or Abaddon Succubus on one of your kill-sites.

Blink/Teleport/Tactical Move

Mainly used to get your Pudge Butchers, Gloam Toads and Nelly Longarms in the right position, but also very handy for Coy Nixies and Abbadon Succubus.

Displace/Led Astray/Lure/Swap

Different ways to manipulate enemy minions. Displace and Swap are very versatile and can be used to reposition your own minions too. It's also easy to get an opponent's artifact into your hands with either of these cards.

Infiltrate

Keep this in your hand for those really big minions that somehow evade your kill-sites. Move them towards your kill sites. Preferably using them to attack your opponent before dragging them into the Void/Bottomless Pit/Mortimer's Den/Thin Ice.

Temptation Island

@oilcorner