What does it mean to support?

People give a lot of different answers to this question.  If you're Janna for a Vayne, your goal is to keep your carry alive and CSing.  If you're Leona for a Corki, your job is to feed your carry kills.  Your job is to keep your carry safe from ganks.  You're supposed to hold bush control.  You should keep your carry at high health.  You should harass the enemy carry.  You should zone the enemy Kog'maw.  You should have good map awareness.

These are all good points, but as far as I'm concerned, support has exactly one job, which can be said in a single sentence.  The job of the support is to snowball your carry relative to the enemy carry.

How to execute this job properly changes with the matchup, and it's when figuring out how to do your job that you arrive at the things mentioned earlier.  If you have a hypercarry and are fighting a midgame carry, just make sure that you keep your carry alive and farming.  If you have a midgame carry and you're fighting a hypercarry, make sure you're killing the enemy carry or at least pushing him out of lane.

Using this description for your role in a team will help you figure out what runes and masteries to run as well as what items to build.  Snowballing your ADC relative to the enemy ADC can mean being as strong as possible early---run flat runes, build early tank or damage, and win your lane really hard.  Or it can mean having good items to help your carry lategame---run some GP10 and build for later.  Every time you make a macro decision in an unfamiliar situation, ask yourself, "What will help me snowball my ADC relative to the enemy ADC?" and do the appropriate thing.