Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
So you've fallen into the depths of your own personal ELO hell, populated by feeders, leavers, ragers, and general baddies. You know you're better than this, and you've decided that by using a hard carry you'll be able to pull yourself out. You're right, and I'll tell you how to do it!
Runes And Masteries
Do NOT, regardless of how good you think you are, take full armor pen quints. Take 2 flat HP quints. These will help you immensely in your laning phase, while balancing damage output with the 1 remaining armor pen quint.
No debating here. Full armor penetration.
Seals and Glyphs
I like to take mana/level for both my seals and quints as they scale with your mana needs, and unless you constantly spam frost you'll never have mana issues. Volley is your best harassing skill early on. This gives you the mana regen to use it whenever you want to harass, or clear minion waves (though more on this later).
Pretty standard 21/0/9. I like to take 15% magic pen for more oomph on my arrow. In the utility tree you won't need more mana or regen because of your runes, and you need all the EXP advantage you can get.
Ghost and flash. You need the escapes and mobility to run away faster or chase people down.
Laning and Beyond
This is crucial. Many games are won or lost at champion select. Talk to your team about who is comfortable with what champions, and try to get a ranged AD, AP, tank, jungler, and another melee or support if possible to round out the team. Remind your teammates to last hit and not push waves so that you (assuming you pick Ashe) and the jungler can gank.
Early game (1-7)
Start with Doran's blade and a health pot. The extra HP from doran's + 2 quints will make Ashe a formidable early game champion. Take a solo lane if you can (mid preferably), as you need to farm. However, as Ashe you can do fine in any lane. Last hit creeps, and harass with volley when you can kill two or more minions and hit the enemy at the same time.
At this phase you need to focus on farming, and not dying. Both of these should take precedence over harassing, but if there aren't any minions to last hit, then use your saved up passive crit and volley to harass.
Once you save up ~1350g (should be around level 7), it's time to push the creeps closer to the enemy tower (spam volley and use up your mana) then blue pill back to buy a pickaxe and level 1 boots.
We now enter the most important part of the game, where you can guarantee your team a victory. You have some speed, a long stun, and a slow. If you're mid, push your creep wave again, go back towards your tower as if you were blue pilling once more, but then go through the jungle to bot lane for a gank. Warn your teammates that you're coming a good minute earlier so that they can heal up and let the enemy push.
Initiate with your arrow on the weaker champion, and with your Q-skill enabled shoot them until they die. If they run into the bushes to try to juke you, use hawkshot for sight, and feel free to use flash and ghost to chase down runners. They won't run away from you.
Hopefully you'll have killed at least one, giving bot lane an advantage. Even if not though, chances are they had to run, and your team can push the tower. Be aware of whether the enemy mid is coming down, and care for the jungler. Remember, better safe than sorry. Don't waste your advantage.
If the mid lane enemy champ didn't come down, at this point he'll be pushing your tower, so head back to push it. Ask your jungler to help you gank if you both have HP. Your arrow should be almost off CD by this point.
Continue farming and ganking in this manner until you finish your Infinity Edge. I like to get the BF sword out of the way first. The money will roll in quickly.
Finish your boots next, Build a zeal (components first if you must, starting with attack speed dagger), and a vamp scepter, and now the mid-game phase should be winding down.
If your teammate gets caught out of position and is being chased, don't hesitate to use your arrow to give him room to escape. Also use volley to slow multiple targets from a safe distance too. And this brings us to...
Kiting: you need to get at least proficient at this. It's your greatest strength, including in teamfights! If it takes enemies a year to get to you and they're losing chunks of HP, they won't bother.
Ganks have become so rampant by now that teams are starting to group up. Buy wards for map control. Remember, every time you gank or see a gank coming because of a ward, it has paid for itself and more.
Build a last whisper, finish your phantom dancer, build a Guardian Angel, and then finish your bloodthirster and buy elixers. Never be alone at this point unless you see all 5 enemy champions thanks to wards, and if you don't, use hawkshot to scout ahead and avoid ganks. Remind your team of this, because fighting 4v5 is not fun.
Fact: This build leaves you very squishy. Because of this, it's imperative that even though you can initiate with your arrow on an enemy out of position, allow your melee/tank to go in first and soak up the CC/burst damage. Once that happens you will be able to quickly whittle down any champion, and in fact the whole team.
Bear in mind there are better survival items than GA, however, its effect is as much psychology as it is utilitarian. When the enemy team sees that even if they "kill" you you'll just come back, they are less likely to target you in a team fight. With good positioning I rarely if ever get targeted for long enough for the GA to even do its magic.
If the game is still going when your build is done, continue buying elixers and remind your team to do the same. You'll be a monster carry at this point, and should have no problem taking any champion down quickly in a teamfight. Spam volley to hit multiple targets who may be further than your normal attack range allows, and toggle Q whenever someone may try to run from you or your teammates (or AT you).
Remember, you deal insane damage, so don't be afraid to use your melee teammates' sacrifices to ace the enemy team. They buy you time, you win them games, and everyone is happy. Let your melee comrades commit first, though again this doesn't mean you can't initiate with a stun. On the contrary, you should initiate if a champ gets separated by even 10feet, with your team ready to pounce, as he will very naturally be focused down by your team, giving you a 5v4 advantage.
Very final tip, your arrow is a stun, and can interrupt pesky ults such as fiddlesticks and karthus. Don't hesitate to use it for this!