Bypassing various factory amps

It's best to have experienced installers around you so you can ask them.

At times you don't need to bypass the factory amps if there's a turn on lead in the factory harness (chrysler/infinity). 

Other times you can wire them up this way, but the system gets too loud too quickly (not much volume control)- some Ford Mach systems.  In these cases, you can sometimes take the RCA signals out the deck, and wire them to the amp inputs on the harness.  Also keep in mind that Ford commonly uses 5 volt turn ons for their amps, so if this applies, use a 1.5k ohm resistor on the turn on lead.  Some times there's no need because the harness is the same at the amp, which is in the center console under the radio- plug and play.  You'll find some Toyotas like this, too.

Older Bose systems in some Nissans (for example) had the amps at each speaker and you had to bypass there.

Many newer vehicles with premium systems have crossovers (and eq settings as well) built into the amps.  Mitsubishis with the amp under the passenger seat are not that fun to learn- have a tone generator handy.  The shop I used to work at had us series the tweeters with the door speakers to present an acceptable 8-ohm load to the new decks.  That's what I consider a "hack" solution.  The problem with this is the front speakers sound quieter compared to the rears (have to fade it forward), and the tweeters are now playing full range.  At times like these, the best thing to do is to use an amp integration harness, or upgrade the speakers and rewire from the new deck.

I could keep going but I won't.  You will learn as time passes what needs to be done.  If you're not sure, just ask one of the more experienced guys in the shop.  You'll also learn who to ask, and who not to ask.  Some people are great at installing, but horrible teachers.