Doran's Shield (used to be the recommend start by Riot, then they changed to Doran's Blade). I like the shield because if you are last-hitting like you should be, then the 3% lifesteal is 0-3 health per shot. Not very useful, as compared to 8 HP regen every 5 seconds, plus 20 extra health and 10 armor (good against minions and other AD champs, like Ashe or Sivir). Now, if they use an AP champ, like Veigar or Vlad at mid (or at top/bot, usually Ashe is mid though), the Shield still protects you from minion damage, plus the health regen means you don't have to worry about staying in range to deal damage to heal faster. Granted, Doran's Blade is good for a heavy harasser Ashe, but I still like the defense.
At any rate, boots come next. Get a BF Sword or Pickaxe, upgrade your boots (Berserker Greaves, Merc Treads (if against lots of CC/AP), or Swiftness (just your preference)), and build that Infinity Edge. You now have the raw firepower to get you through the mid-game. You should grab Zeal, then Last Whisper. Upgrade you Zeal to a Phantom Dancer, and grab a Banshee Veil if you need it (maybe earlier if enemy mages are fed).
For the last 1-2 items, I usually grab Black Cleaver (if a teammate doesn't have it), Bloodthirster, another Phantom Dancer, or Brutalizer --> Ghostblade (maybe Madred's Bloodrazor as well), depending on the team I am facing. If I need to be slowing a lot, then I will go for some Attack Speed with a Phantom Dancer/Black Cleaver to make sure my targets don't go anywhere with my Frost Shot. If I need to penetrate more Armor, Ghostblade adds APen, with some Crit Chance and Damage, plus the active (movement/attack speed buff for 4 seconds). If I seem to be dying in teamfights, a Bloodthirster might keep me alive with lifesteal (getting the cap with Ashe isn't hard. Minions die pretty quickly at higher levels). If I have an AD-based team, Black Cleaver reduces the armor of enemy champs, letting my team do more damage to them. Also, Madred's Bloodrazor works well against enemies will no Magic Resist, since you can just autoattack them to death with high attack speeds and magic damage, plus great AD and crits.
TL;DR: Doran's Shield, basic Boots, IE, upgraded Boots,Phantom Dancer, Last Whisper, Banshee's Veil/another defensive item (if needed), final item (Bloodthirster, Black Cleaver, Ghostblade, another Phantom Dancer, Madred's Bloodrazor). The recommended items are rather spot-on, minus the order and the Doran's Blade
Dan Dinh's guide on cooldown Ashe is pretty good. That's where I got the idea to use Ghostblade from. For my suggestion, you may want to get the Brutalizer earlier and wait on the Ghostblade, like Dan Dinh suggests in his guide, since the Ghostblade doesn't add much a Phantom Dancer or IE couldn't add better.
And in response to xpsychedelico two posts above, AS is mainly since she is dependent on her autoattack. If you wait for her passive to take effect (3 seconds) in a team fight, you will be dead before you can put off three shots, if that many. It's really an early-game thing. Sure, the first attack in a teamfight will be a crit, but then you have to rely n items/masteries/runes to get the rest of the crit chance. Of course, rushing AS isn't good on Ashe, since AS without AD is pointless. IE is the best thing to get first, then go for AS/Crit Chance, finishing with APen/AReduction, more AD, and whatever else fits the situation.