I've been stumped and confused in this rom a few times, but I generally am able to figure out how to progress after a while. This forum topic is pretty long so I'm sorry if this question has been answered.
I've gotten to the point where I just saved Yellow from the pokemon that was attacking her. After this, the dialogue mentions me teaching her how to capture a pokemon and she joins me. I'm not sure what to do after this point. The things I've tried include:
Capturing a Caterpie in the forest
Capturing a Rattata outside of the forest
Doing both of these events, but with an empty slot in the party.
Wandering around in the area around where I saved her.
Talking to the villagers that are fretting over Yellow's absence.
I will admit that I don't quite remember if a caterpie or a rattata were Yellow's first pokemon.
EDIT:
I continued searching, and found a screenshot that pertained to this. I just didn't look hard enough in the forest, apparently! I have a habit of getting stuck in games.