The following legendaries can be found in the base game of Pokemon Scarlet and Violet. There aren't many legendaries available compared to recent games, but the Hidden Treasure of Area Zero DLC greatly expands the number of available legendary Pokemon.
You will first get Koraidon very early in Pokemon Scarlet on Poco Path as part of the story. You'll be able to ride this Pokemon, but won't be able to battle with it until you restore its power completely. From then you can switch between it's rideable and battle forms, but it does not behave like a normal Pokemon that you can trade or transfer out of the game.
You will first get Miraidon very early in Pokemon Violet on Poco Path as part of the story. You'll be able to ride this Pokemon, but won't be able to battle with it until you restore its power completely. From then you can switch between it's rideable and battle forms, but it does not behave like a normal Pokemon that you can trade or transfer out of the game.
After finishing the main story of the game you will be able to find a second Koraidon in Pokemon Scarlet outside of the Zero Lab where you defeated it before. This Koraidon behaves as a normal legendary encounter where you can battle and catch it. It cannot be ridden but can be traded and transfered just like any other Pokemon.
After finishing the main story of the game you will be able to find a second Miraidon in Pokemon Violet outside of the Zero Lab where you defeated it before. This Miraidon behaves as a normal legendary encounter where you can battle and catch it. It cannot be ridden but can be traded and transfered just like any other Pokemon.
The following four Pokemon are known as the "Treasures of Ruin" set of legendaries. In order to find and catch each one, you'll need to find and pull out eight stakes that seal the shrine containing the legendary. If you take the history classes offered at your respective academy, you can learn all about them and the shrine locations will appear on your map. However this is not required to catch them and all the shrine and stake locations can be found below.
After finding and removing all eight stakes found in southeast Paldea, you will open the Grasswither Shrine in South Province (Area One). Inside the shrine you can find and catch Wo-Chien.
After finding and removing all eight stakes found in western Paldea, you will open the Icerend Shrine in West Province (Area One). Inside the shrine you can find and catch Chien-Pao.
After finding and removing all eight stakes found in northwest Paldea, you will open the Groundblight Shrine on the Socarrat Trail. Inside the shrine you can find and catch Ting-Lu.
After finding and removing all eight stakes found in western Paldea, you will open the Icerend Shrine in West Province (Area One). Inside the shrine you can find and catch Chi-Yu.
The following legendaries can be found in the Kitakami region, the first part of the Hidden Treasure of Area Zero DLC. They all serve an important role in the story of the DLC.
Ogerpon will be found as part of the main story of the Teal Mask DLC. You'll need to defeat Kieran in battle before you get a chance to battle Ogerpon itself. It is a titan-like battle where Ogerpon will cycle through each of it's possible masks. After defeating it in battle, you will get a guaranteed catch with whatever ball you'd like to use.
In the main story of the Teal Mask DLC, you'll need to find and defeat Okidogi in battle. Once the story wraps up, you can return to this same location to battle and catch it like a typical legendary encounter. It can be found in the Paradise Barrens of Kitakami near the fly spot.
In the main story of the Teal Mask DLC, you'll need to find and defeat Munkidori in battle. Once the story wraps up, you can return to this same location to battle and catch it like a typical legendary encounter. It can be found near the lake in the Wistful Fields of Kitakami.
In the main story of the Teal Mask DLC, you'll need to find and defeat Fezandipiti in battle. Once the story wraps up, you can return to this same location to battle and catch it like a typical legendary encounter. It can be found on a cliff ledge that can be reached by exiting the bottom of the Chilling Waterhead caverns of Kitakami.
To find Meloetta, you must head east from the Coastal Outdoor Classroom in the Coastal Biome. You'll notice leaves spinning in a large circle in the wind in this area. You'll need to find the source of this wind cyclone, which is a small bush. Once here you must spin clockwise for at least 10 seconds and then pull out your camera and apply the Sepia filter. Meloetta will then appear and play their Relic Song. From here it can be battled and caught like any other legendary encounter.
Terapagos can be found during the main story of the Indigo Disk DLC legendaries. After you become the Blueberry League Champion you will go on an adventure to explore Area Zero and find it's hidden treasure, which is Terapagos. You'll need to defeat it in a titan-like battle with the help of Carmine and Kieran. Once defeated you will get a guaranteed catch with whatever ball you'd like to use.
Pecharunt can be found as the third and final part of the Hidden Treasure of Area Zero DLC during the Epilogue aka Mochi Madness. This part of the DLC can be triggered by taking a Mythical Pecha Berry from a mystery gift distribution to Peachy's shop in Kitakami and interacting with the plushie. At the end of the Mochi Madness storyline you will battle Pecharunt in a titan-like battle. Once defeated you will get a guaranteed catch with whatever ball you'd like to use.
After completing the main story of part two of The Hidden Treasure of Area Zero DLC, you'll find a man named Snacksworth outside Blueberry Academy. Each of Snacksworth's Legendary Pokemon can be found after you obtain the treats he gives you for doing BBQs in the Terarium. Each legendary can be found at a different location spread throughout the original Paldea map. Each encounter will be at Lv. 70 except Kubfu, who will be Lv. 30.
Some of these treats are obtained by completing solo quests and some are obtained by completing group quests, and those are different depending on your version of the game. However they can all be obtained in either version of the game if you complete all the solo and group quests. They are broken down as follows:
On the northern shore of the lake to the west of Montenevera.
On top of the Poco Path Lighthouse.
On top of a cliff in the northern part of Asado Desert.
On the north side of the mountain lake in West Province (Area One).
On the far eastern edge of on a cliff in East Province (Area Three).
On the edge of an island on the western side of Casseroya Lake.
In the water next to a tiny island in the North Paldean Sea.
On a hill between the large cliff and river on the western side of South Province (Area Four).
On a beach in the south of South Province (Area Four).
Next to a lake in a canyon near Firescourge Shrine in North Province (Area Two).
Just off the coast of the western portion of the North Paldean Sea. Right next to the Gracia Stones.
In a southeast crevice at the very top section of Alfornada Cavern.
On a ridge bordering the Great Crater of Paldea in South Province (Area Three).
On a grassy ledge next to Fury Falls in North Province (Area Two).
On a grassy ledge next to the Great Crater of Paldea in West Province (Area One).
In the north-east corner of Tagtree Thicket.
On a grassy ledge next to a waterfall bordering The Great Crater of Paldea in East Province (Area Two).
On the southeast side of a giant rock plateau in South Province (Area Five).
In the bottom part of a cave to the northwest of the Dalizapa Passage Pokemon Center.
On top of the roof of the Pokemon League building.
On the edge of a cliff to the south-west of Casseroya Lake.
On the rocky area just south of Socarrat Trail. Just to the east of Groundblight Shrine.
Right at the Fury Falls flying location in North Province (Area Two).
On a snowy hillside to the north of the ruins in the southern area of Glaseado Mountain.
Next to some ruins that border the Great Crater of Paldea to the north. On the southern part of the mountain that surrounds the Dalizapa Passage Pokemon Center.
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