You bought yourself a Pokemon Sapphire and are now ready to tackle the wandering Legendary Pokémon very much like the Legendary Dogs in G / S / C. It should be noted that this will be really hard. Although everyone says that Latias can accidentally appear in any location, there are places where the chance of catching this wandering Pokemon is much higher.
Steps
Method 1 of 2: The winding path

Step 1. Get all 8 badges and beat the Elite Four
You will not be able to catch Latias until you have met these requirements.

Step 2. After the end credits are over, when you are at your house in Littleroot, go downstairs and watch TV
You will learn about a red flying Pokémon that wanders around Hohenn (it is obviously Latias).

Step 3. Go upstairs and if you put the Masterball into the computer, take it out
If not, be sure to get it. If you haven't spent it before, go to step 6.

Step 4. If you have spent your Masterball on Kyogre or Reikuazu, you will have a more difficult task
Take Trapinch or High Level Wobbuffet. Better yet, a high-level Pokémon with the Evil Eyes skill (for example, Zubat or Golbat from Victory Road). Give a Pokémon with the Evil Eyes skill a Quick Claw and spend some money on a few Carbos so that your Pokémon has the fastest speed. Put this Pokemon at the top of your group.

Step 5. Buy a huge amount of ultraballs

Step 6. Be sure to take a Pokémon with the Surf skill and the Fly skill with you

Step 7. Fly to Movil
Head east and cross the river on Route 118. Head east across the grass to the path where the Berry Master's house is. Stand on the east side of the house. It's raining? If so, then you are in luck. If it is not raining, check Important in the Tips section.

Step 8. Usually it doesn't rain here
Now you need to go to Lilikov.

Step 9. Travel east on Route 121 to Mount Pyre
Head to Berry Master's house, but stay at the top of the path to reach a small pond next to his house.

Step 10. Swim in this pond
Meet six or seven Pokémon until you reach Latias. Although the chance that you will now meet him is rather low.

Step 11. After a few battles, head west again past the Berry Master's house to get to the next path

Step 12. When you just get on the path, you will see a patch of grass
Look in it. If you're lucky, you will encounter Latias after a few battles. If you do not find her after 8 meetings, go back to Lilikov and repeat everything from the beginning until you find her. Location plus a quick change of your location should lead to your soon meeting.

Step 13. When you meet her, immediately throw a masterball at her
Congratulations!

Step 14. If you spent it, immediately use the Evil Eyes skill
If you got Trapinch or Wobbuffet, reduce her health and start throwing ultra balls. If you kill her, restart the game. If she runs away, you can track her with your Pokedex, just like you were able to track the legendary dogs in G / S / C.
Method 2 of 2: Swimming in the sea to catch Latias and Latios

Step 1. Win the league

Step 2. After the end credits, you will learn from the TV that a blue or red Pokémon has been spotted
If you are playing the Sapphire version the Pokémon will be red, and if you are Ruby it will be blue.

Step 3. Travel to the city of Mossdeep
Swim left and down until you find yourself on Path 126.

Step 4. Fight several wild Pokémon
If you haven't met Latios or Datias, swim back to Route 124 and face off against a couple more Pokémon.

Step 5. Ultimately, you should meet a flying Legendary Pokemon that matches your version of the game
Advice
- Note: It always rains outside Berry Master's house, but this has nothing to do with flying Legendary Pokémon.
- Important: If it was not raining outside the Berry Master's house, then you must do something else. Check each Hoenn Trail and look for a trail that does rain, although it usually shouldn't (the places where it usually should rain are Route 119 and the southern half of Route 120). When you find unusual rain, come up with a similar scheme for capturing Latias, which would start from this location. Search the area where it is raining to meet 6-7 Wild Pokémon, and then go to the nearest Path and meet with eight more Pokémon. Repeat until you find Latias. If there are no Ways with unusual rain, continue following the method as if it were raining outside the Berry Master's house. In the end, it should still work.
- Latios and Latias have places where you can find them quickly. It's best to use trial and error and memorize the steps you take.
- Don't be upset if you don't find it quickly. If you're unlucky, it may take some time to capture.