Looking to Expand My Competitive League Playing Knowledge

From a simple player to hopefully a pro player, I am hoping to learn the ins and outs of league on the competitive side, most specificly the champion select side of things. I'd like to know 1) how do you know what champions syngergize well together, for a team, for bot lane, between lanes, jungle, wherever champions synergize, and if I'm looking to do a specific style what should i be looking for to achieve this? 2) I'd like to know what exactly runs through a competitive scene team's minds when it comes to the champion select, what are they looking for when they pick champions, what makes them pick champs in certain orders. What should be looked at when the enemy team is picking their champions? What about for building a specific team composition? simply put, what is the checklist so to speak that you run through when going through champion select in team?