The most reliable way to find the Pig King is to follow the roads and trails scattered throughout the game. These roads and trails sometimes lead to Pig Villages, which is a collection of huts and occupied by several Pigmen. Normally, if the Pig King spawned at all, he’d be close to a Pig Village. Do note that not all worlds generated by the game have a Pig King in it, since sometimes there isn’t enough room for the Pig King to be generated in the game. The Pig King’s appearance is that of a very large pig with a crown made of dried grass lying down on a wooden floor and surrounded by black pillars.
After setting the Traps, check it regularly. A Trap looks like a normal stick-and-basket trap, and when you’ve caught something, the basket will be on the ground and shaking constantly. If you click on a shaking Trap, you can gather both the rabbit and the Trap, if you have space in your inventory, and you can kill the Rabbit right off the bat by right-clicking it. You now have your meat. Get Rabbits trapped in your other Traps, and kill them for more meat. Set the Traps again to get more Rabbits, ensuring a steady supply of meat. Rabbits normally spawn at morning, but the best time to check Traps would be around dusk. Traps, however, wear out eventually, and you’ll be forced to keep making them to replace the broken ones and using up precious resources in the process.
Once the eggs become a den, simply walk up to it and a Spider or two will emerge to attack you. Attacking one will alert other Spiders in the den, and they’ll all emerge to try to kill you. Lure them to the nearest Pig, hitting them every now and then with your chosen weapon to ensure they’re still following you, and the Pigs will start attacking it. The more Dens and the higher the Den’s tier, the more Spiders will come out at once, giving you a steady supply of Meat and Pig Skin from the unlucky slain Pigs, and Monster Meat, Silk and Spider Glands from the Spiders. Once the assault of the Spiders are over, you can then feed the Monster Meat to some Pigs, which earns their trust and lets them follow you around for a while. Feed them too many Monster Meats, and they turn into Werepigs, making them aggressive and attacking everyone in the area, even other Pigs. Once a Werepig attacks a Pig, the entire village will attack it, and with luck, they’ll finish each other off without you having to lift a finger to help. Werepigs still drop Meat and Pig Skins, though, and are a slightly more reliable way of making sure Meat drops since they drop 1 Meat and 1 Pig Skin consistently upon death, unlike the common Pig’s drop rate of 75% Meat and 25% Pig Skin. You don’t even need to keep attacking the Spiders and Werepigs after luring them into the village; the normal Pigs can do that for you, and both the village and the den respawn their respective denizens eventually, providing you a steady stream of resources.
The items you might dig up from graves include knots, buttons, toys, and a lawn gnome, which apparently amuses the Pig King immensely, judging by the amount of Gold he hands you. Graves, and therefore items from them, are non-renewable and scarce in the original game, however, and must be considered as a sort of last resort if you need a lot of Gold at once. In the Reign of the Giants DLC of the PC edition and the console edition, these items can sometimes be found by breaking open Tumbleweeds in the Desert, but it’s still not very reliable despite the yield.
You can sometimes trigger earthquakes by detonating Gunpowder and Slurtle Slime while in the Caverns. You can make Gunpowder by combining a Rotten Egg, Charcoal, and Nitre, and you can get Slurtle Slime by killing Slurtles, which look like an odd combination of turtle and slug, or feeding them plenty of Rocks.