PTA is a game made by and for the residents of the 4chan
/tg/ forums, so it's a "you know how to play because you witnessed its birth" kind of situation. There might be a tutorial somewhere, but it's unlikely.
You could try reading through the Q&A threads, and the actual play threads that constitute the raison d'être of the game. These are archived under the pokemon tag on /tg/.
The closest I came to a tutorial there was this explanation by the creator, in answer to a question about how the game is going to work (this was before the PDF was published):
Dr. Mr. Stark !!d0diDeRpO0s 08/03/09(Mon)23:23 No.5330789
I'll try to sum it up at neatly as I can.
There are currently 7 trainer classes that you can take.
Ace Trainer, Breeder, Researcher, Capture Specialist, Coordinator, Psychic and Martial Artist.
They each play different roles in a traveling party.
You travel throughout whatever region you like and the GM provides wilds and NPC battles. Wild encounters are not one at a time. For example, a common encounter would be five pidgeys, two pigeottos, and one pigeot.
Players play through the game how ever they'd like and the GM provides challenges.
For example, my playtesters currently flew into Sinnoh to take on Galactic who had stolen Blaine's pokeflute loaned to Blaine from Mr. Fuji. They are slowly realizing the crap they've gotten themselves into and may be realizing they are in over their heads.
Players capture pokemon with pokeballs and use their trainer feats (with exclusive powers to each class) to make their pokemon better then their fellow party members, while still working together.
It seems like PTA assumes you have enough familiarity with the Pokémon video games to already know in general how it's supposed to play, and then it adjusts that play experience to accommodate a PC party rather than the solo play of the video games.
Off-topic, there is a 1d4chan wiki artile on it: Pokemon Tabletop Adventures that you might find helpful/useful. This collection of links contains the necessary documents.