No, as far as I know the methods to evolve both Malamar and Goodra are not explained in the game.
Although Inkays's evolution method it is hinted at seeing as Inkay is known as the "Revolving Pokémon," Malamar is known as "Overturning Pokémon" and learns the signature move "Topsy Turvy."
Sliggoo's evolution method is also hinted at by a Trainer Tip on Route 17 which says: "Some Pokémon may evolve if they gain a level while it is raining." Given that tip, the fact that Goomy is found in a swamp, and can have the ability Hydration, it wouldn't be a huge leap in logic to assume the sign could possibly be referring to Sliggoo.
I'm sure both of the evolutions will be shown at some point in the anime which is most likely the way the evolutionary methods were originally intended to be announced by the creators.
To evolve into Malamar you must hold your DS sysem upside down while leveling up Inkay to level 30 or higher.
To evolve into Goodra you must level up Sliggoo to level 50 or higher while you are in an area in the overworld where it is raining. (Note: rain started by Rain Dance/Drizzle will not allow Sliggoo to evolve)