UPDATE: As it turns out, the rare Pokemon you can catch via Island Scan is based on the day and island you're on when you use it. Here's a short chart of what you can get:
Day | Melemele Island | Akala Island | Ula'ula Island | Poni Island |
Sunday | Cyndaquil | Gothita | Rhyhorn | Elektross |
Monday | Totodile | Spheal | Swinub | Conkeldurr |
Tuesday | Deino | Luxio | Duosion | Togekiss |
Wednesday | Horsea | Honedge | Roselia | Leavanny |
Thursday | Klink | Venipede | Staravia | Serperior |
Friday | Chikorita | Bellsprout | Vigoroth | Samurott |
Saturday | Litwick | Marill | Axew | Emboar |
ORIGINAL STORY: In Pokémon Sun and Moon, there are several popular Pokémon that aren't naturally found in the Alola region, including but not limited to Charmander, Squirtle, and Bulbasaur.
However, that doesn't mean you don't have a chance to capture them.
How To Catch Rare Pokémon
Step 1: Progress in the game far enough that you unlock the QR Scanner option in the menu, which doesn't take that long at all.
Step 2: When everything's set up, scan 10 Pokémon QR codes to get the skill Island Scan.
Each Pokémon has a unique QR code, and that includes the shiny versions. For example, a Rowlet will have a different code from a shiny Rowlet.
Remember, you can only scan 10 times per day, and that means you can use Island Scan only once a day too.
Note: If you're having trouble finding enough QR codes to scan, there's a massive collection over at Imgur that you can use.
However, in case that gets pulled down, some Pokémon Sun and Moon players have reported that scanning any kind of QR code will also work.
Step 3: Use the Island Scan ability to locate a rare Pokémon that isn't normally seen in the Alola region, and that includes Charmander, Squirtle, Bulbasaur or any other Pokémon from the first generation and up.
Step 4: Head to the location of the Pokémon that Island Scan found. Take note you have only one hour to go there and encounter it before it disappears.
On top of that, you'll only come across it ONCE. If it runs away or if you accidentally defeat it, you're going to have to wait until the next day to try your luck again, and that's because you can scan only 10 QR codes and use Island Scan once a day, as mentioned earlier.
Step 5: Needless to say, just repeat steps 1 to 4 until you get the Pokémon you want.
Now, unless you're very lucky, it's going to take a lot of patience until the Island Scan feature will locate the exact Pokémon you're looking for, but as everyone can imagine, it's worth it.
With all said and done, don't forget to hit up our other Pokémon Sun and Moon guides on how to evolve Eevee into Sylveon, Leafeon, Glaceon, and more; where to find Eevee, Pikachu and Growlithe; how to catch a shiny Pokémon easily; how to get all the legendaries and Ultra Beasts; and how to increase happiness quickly.