i.e. paying attention. As long as it won´t hinder you to progress, it shouldn´t be a problem. Maybe watch TV again in San Francisco, because it tells you what you want to do with the crystal.
You know, just to stop you from asking “Why would Zak do that with the crystal?” in the future.
I assume you have unlocked the blue crystal from its pedestal.
After all that effort, you don’t want to pick it up? You are a reporter who wants to win the Pulitzer, you have in your hands a crystal of unknown origin… it’s a scoop!
But… when Zak picks the crystal up, it says: "It’s an artifact "
OK, go to your living room and turn on the TV…
Mhhhh, should I take it or just leave it and go home?
Well, in Zak you can do both! 
That good suggestion unfortunately came after I saw the dream. And you know what? That machine with the crystals appears for just half a second.
I’ve not done much. I took the crystal, then shit happened and I don’t know why. Some alien guy came and took me in the mindbending machine. I have understood nothing of what just happened and the only positive information that I got is that I didn’t pay for the flight back to SF, which might be useful in the future to save money.
Now, I’m slowly deciding if I should try to get the crystal back or do another random thing for no reason whatsoever.
Do you skip cutscenes for some reason?
You want it and everything you need for that, you will find in San Francisco.
That was the “Alien Mindbender”
OK, you still don’t know too much, but you know that you have an artifact in your hands.
Watch the TV…
David Fox put everything there for a precise reason.
Everything will be clear soon.
Yes, I got the “artifact” thing, but you guys should know that the TV talks about the artifact only the first time you watch it. Now it’s in a neverending loop about the wave of idiocy and the telephone hum.
No. What I meant is that I didn’t have any information about the fact that touching the pedestal would have triggered Mr. Potatoface.
That´s been an issue that was still in Monkey Island 2(when even Ron stumbled over his own Kate Capsize Puzzle). Most of the information gets never repeated. That´s the issue with those older games.
The following cutscene where the alien disguises himself and leaves to go after you should be enough to tell you that, and after that you have time enough to leave. But the way you did it, was indeed better.
Actually, I’m OK with the TV not repeating the same program. I remember most of the dream and what was on the TV at the beginning, and I will take notes anyway.
I have more issues to find a goal. I know/imagine what I should do with the blue crystal but I don’t understand why I should do it, what’s the final goal of it.
Yes, that’s my point: you discover why it happened only after you have done it. It happened by chance.
If the chance to meet the literal woman of your dreams isn´t enough incentive for you, I have no idea what you consider a good reason to do anything.
Frodo didn´t now the Ringwraiths would be after him the first time he put on the ring.
Just quickly start a new game to refresh your memory of your dream plus the TV program. And what was in between.
OMG! I am now scared of this game! Reading this thread makes it clear to me that I have no chance at getting anywhere with this game. 
dZ.
So, now things are more clear, finally the game gave me a goal. That’s much better.
If you are, where I think you are. That is the first of 2-3 exposition dumps you get in the game. There is another one late in the game that is optional but will tell you a lot about the backround of everything that is happening.
That’s why I love this game so much. Walking around doing random things can be very rewarding. I think the Lucas games were the best for programming jokes to appear for many things that have nothing to do with the end goal.
I was at Annie’s and she explained to me a bit of the story. Now I’ve become four people, one of which explained to me that she puked in zero-g.
Fun! 
Yes, that’s true.
But you didn’t die. You have learned that crystal is fottutamenting important, if those potatoface wanted it.
Nothing is lost, you know? You can find a way (more than one is available) to take it back.