Yarok and
Doubling Season are fundamentally different effects that don't interact with each other at all.
Yarok says that if an ETB trigger triggers, it triggers twice. This means anything that says "When <this thing> enters the battlefield," or "Whenever a <whatever> enters the battlefield" gets doubled. So yes,
Invasion of Zendikar now gets you two lands twice, for four lands. If you have a
Landfall card out, that gets doubled too, so you actually get eight triggers.
Doubling Season is a replacement effect. If you would create tokens, though any means, you create twice as many instead. If you would put counters on something, through any means, you put twice as many instead.
Now, if an ETB trigger creates tokens or puts counters, then it will get doubled up by Yarok
and by
Doubling Season. Just, for different reasons.
Mostly, Yarok is just "ETB? Double it"... that's not super interesting. Whether that's
Ravenous Chupacabra,
Mulldrifter,
Reclamation Sage,
Omen of the Dead, whatever, we've seen this before. The one
weird interaction I can think of is
Isochron Scepter, because doubling that ETB means that you get two cards exiled, and the weirdness of Magic rules means that you get to cast
both of them when you activate the stick. I actually built a whole deck around this; turns out that if you put a
Mana Drain AND a
Word of Command under a Sceptre, it makes people cry. Then again, just a regular
Word of Command does that, because who's got the time to read all that text?