Clarification on the Brewing process, what happens when.

I've never brewed a beer (only mead) so this may seem silly.
At what point does carbonation occur? This may come naturally to beer brewers but everything I've read gives me the impression: it just happens... but how?
I have a bucket... I have carboy... I even have grolsch style bottles I bought.
Some articles mention priming sugar... some dont.
So... I pour apple juice in... pitch some yeast and wait.
Will it carbonate in my bucket? my carboy secondary? in bottles only?

Another side question: Are there tannins in store juice? do I need to add tea?

Yeast plus sugar (or apple juice/cider) equals alcohol a co2. When your cider is fermenting, it should be under airlock and you will see the co2 being produced, and possibly even smell it being release from the primary. To answer your question, in order to carbonate you need to harness this co2 in one way or another and force it into solution. You can either keg and force carb or once racked to secondary, bottle and add some form of fermentable sugar to awaken the yeast and create more co2. When being done in the bottle you need to stop it once desired level of carbonation is achieved or you made a bomb. See the stovetop sticky for how to on bottle carbing. Hope that helped.

sooo what if I bottled while it was still fermenting? is that what the priming sugar is for? let it finish... add a bit in the bottle, and bubbles.

Correct, you could bottle while around 1.010 SG, assuming the yeast you used ferments dry (probably will) it will continue in bottle and carbonate. Just be sure to also bottle a plastic water bottle of it so u can pasteurize or cold crash the glass bottles when the plastic bottle gets rock hard. (Refer to sticky I mentioned)

I did read the sticky... (several really)
The trick seems to be getting it sweet.. getting it carbed... stopping the fermentation process before eating a face full of glass.
I just bought 3 1-gal bottles (glass even ) of Apple juice from Whole foods.
Ill buy some airlocks tonight.
I have a Red Star Cotes du Blanc packet and a Red Star Montrechet(sp)
I figure fermenting till 1.020... bottle it in the grolsch bottles I have.
Keep a plastic bottle as a tester.
Stove top pasturize when the tester is turgid (I have an 18-qt stock pot I use to make my dog's food)
Cool the bottles...

Do I have it down or am I missing something?
Should I use tannins or pectic enzyme additive?

That sounds like a solid plan bro, be sure to sanitize the hell out of everything and it should wrk just fine, I actually have a 7 gallon batch of whole foods aj going right now. Just be aware of te volume in your grolsch bottles compared to the volume of your plastic testing bottle, to keep the pressure gauge as accurate as u can.

Because the whole foods aj is kinda tasty and has no tartness, I added raisins as an experiment to my batch, but its just about ready to be racked to secondary so I can't speak to its effectiveness of making whole foods AJ better as a finished cider. I've heard of people using tea bags, but that's beyond my experience just yet

Edit: plz delete accidental double post