a small structure with outsized loot
A Pyramid is a solid block of Sandstone Brick buried in desert sand with a single zigzag corridor folding down to one treasure room. Most of it sits underground and the tip is normally hidden, so you can walk across one without ever knowing it was there. Inside are banners, a lot of pots and coin stashes, and one chest at the bottom.
what the chest holds
The main item is where the value sits. The Flying Carpet gives you a few seconds of hovering flight on demand, which in pre-Hardmode is close to cheating. It crosses chasms, cancels falls and lets you stall in mid air during a boss fight, and nothing else at that stage does any of it.
The Sandstorm in a Bottle is a very tall extra jump and the desert branch of the accessory chain that eventually merges into the Bundle of Balloons, by way of the Sandstorm in a Balloon. The Pharaoh's Mask and Robe are vanity, and if that is what you drew, the pots on the way down probably paid better than the chest did.
break every pot
Pyramid pots are not ordinary pots. They carry the best Coin Portal odds anywhere in the game, one in 125, and a portal pours out a stream of coins for nothing. No other structure makes smashing scenery worth this much, so clear the corridor properly on the way down instead of sprinting past it to the chest.
how rare they actually are
Rarer than the headline number suggests. Pyramids are only attempted inside Dunes, the smaller desert patches that have no Underground Desert beneath them, and each Dunes biome gets an eighty percent roll for one attempt. That attempt then has to survive a list of placement checks: clear of the world edges, above the surface line, resting on pure sand, far enough from any Pyramid already placed, and a long way from the Dungeon. Fail any check and there is no retry, the attempt is simply spent. Plenty of worlds end up with none at all.
Three seeds change the odds. Sandy britches makes them common, drunk worlds roll the attempt on every Dunes biome and halve the spacing requirement, and Celebration Mk 10 always builds one over the entrance to the main Underground Desert.
finding one
Start by ruling out half the world. Nothing generates in the stretch between the Dungeon and the ocean behind it, and nothing generates within roughly 630 tiles of the Dungeon on a small world, 960 on a medium or 1260 on a large. Whichever side your Dungeon is on, search the other way.
The tip normally sits 13 to 19 blocks under the sand, and the shallowest a tip can ever be is 4 feet on the depth meter, which is barely below the surface line. That is close enough for two tricks to work. Switching lighting from white to retro flashes tiles brighter for a moment, which can outline buried brick. Better, sweep the housing query across the sand: the zigzag corridor registers as a run of enclosed rooms where plain sand registers as nothing.
Sometimes the tip pokes out on its own. And because the main Desert and any Oases generate after the Dunes, a Pyramid can end up buried inside the Underground Desert or under an oasis instead of out in open sand, which is where people give up looking.
keeping one
Sandstone Brick cannot be converted by Corruption, Crimson or Hallow. A Pyramid standing in the path of a Hardmode stripe is a plug in the ground, and the bricks are worth mining out and rebuilding as a barrier wall somewhere you actually need one. Corridor and all, it also makes a reasonable desert base once you light it.