I believe, and someone may correct me in this instance if the conclusions I've drawn are divorced from the fact of the matter, that it's partially the technology. The TM, or Technical Machine, that is used by most Pokémon students to become Human comes equipped with the language. TMs are used generally to learn moves as a Pokémon that they might not normally know. Thunderpunch on a Charizard for example, or Bulldoze for a Venusaur. It implants data directly into the Pokémon's brain to allow for practical application of these techniques and I believe it does the same for language. The other part of it is that most Pokémon - especially those who've grown up around Humans - have an understanding of the language already. They just lack the physical ability to reproduce the words. This, of course, isn't the case for Psychics and Ghosts, who can communicate in our tongue even without human vocal chords. In some cases, at least.