In the Pokemon: Let's Go games, you could obtain Alolan forms of pokemon by trading with NPCs. Are there similar NPCs in Pokemon Sword and Shield, or some other way to obtain Alolan Pokemon?
As LamaDelRay pointed out, an Alolan Meowth can be found in one of the camps. This camp is located on Route 7, and is known as “Renee’s Camp”
However, at the time of writing, you cannot obtain Alolan forms within Sword and Shield for yourself. There are NPCs you can trade with to swap their normal forms for their Galarian forms (or vice-versa dpending on the NPC), but not Alolan forms.
It might be possible to obtain Alolan forms in the future with Pokémon Home coming in 2020. Pokémon Home will be cloud-based storage which you connect various Pokémon games, and it has been confirmed Sword and Shield to be able to both deposit and withdraw from the storage. However, it's merely speculation at this point.
Alolan ninetails is coded into the game as a raid battle on the island’s peak in the lake of outrage but is still currently unobtainable. It most likely will be part of a future event like G-max Snorlax. By that logic you can assume that the others will be too. All Alolans forms have Pokédex entries (excluding cut Pokemon) that talk about their location in galar. Shield stating “ While it will guide travelers who get lost on a snowy mountain down to the mountain's base, it won't forgive anyone who harms nature.”