Kiting is really important to doing well with ranged attack damage carries like Ashe and Varus. All attack and spell cast animations have a junk portion that you can interrupt without stopping the ability or attack (generally you need to play half the animation for anything to happen, then the other half is mostly for aesthetics). Learning what parts you can cut out will make kiting easier, allowing you to attack then immediately move away, attack then immediately move away. Also, it's important to note most melee champions are capable of bursting down half your health once they engage in melee combat with you - so even if they have a sliver of health left it's better to keep your distance.
Beyond basic kiting, status bonuses provided by items and runes have vastly different costs for accomplishing the same thing. Raw Attack Damage is by far the most affordable attribute of the physical damage stats. Most attack damage carries have a little over 100 damage and 1.0 attacks per second at level 18, were a 100 attack damage boost gives a very real 100% DPS bump - you'd need 100% critical strike chance, 100 armor penetration, ~167% attack speed, 200% critical strike damage (at 100% critical strike chance), 75% armor penetration (against 200 armor), or 100 armor penetration (against 100 armor) to gain the same 100% to DPS bonus. Attack speed generally only benefits your DPS by ~67% of it's listed % value at level 18 because it only uses your level 1 attack speed - all other level up bonuses are simply added to the item bonuses rather than used as a base, and you generally start off with 0.667 attacks per second. Anyways, all these will grant a % bonus to your DPS and stack multiplicativly with each other, which is nice - and at a certain point makes stacking raw AD less cost-efficient than applying different stats. Generally the best ADC build right now is still Infinity Edge, Phantom Dancer, Last Whsiper, and Sanguine Blade. Which sort of makes building attack damage carries a little boring. If you want a solid chunk of life-steal Exacutioner's Calling isn't bad either, even if you stack them.
For Yi, most Dominion matches barely skirt the point were building Ability Power makes him less viable end-game, so I'd highly recommend going the Ability Power rotue with him. If you go Attack Damage I'd recommend building Youmuu's Ghostblade, Black Cleaver, and stack Exacutioner's Callings.
As for general strategies, if you are winning try to defend the points you have, if you are loosing to an enemy team's pack of doom sneak to the other side of the map and try neutralizing a point. Doing so forces them to spread out if nothing else, and allows your suicidal allies to start 1 vs. 1ing or 2 vs. 2ing rather than 1 vs. 4ing upon respawning, the latter of which will almost certainly lead to a loss.
Also, if you're finding yourself out of position and getting killed by yourself I'd highly recommend picking up Boots of Mobility until you figure out exactly were your champion needs to be, they allow you to escape bad situations relatively unscathed and are pretty good for learning were you need to be. Even in team fights it's nice to be able to get out of a cool hiding spot that is pointless to be in faster. Once you figure out were you need to be, pick up Merc treads or Ninja Tabi