The purpose of this build is to gives you lots of attack speed and damage together. The reason you would want attack speed on Ashe is because of her Q, which is an on-hit slow. You can slow people a lot faster with an attack speed build, making it harder for them to get away. With this build, you also get a very high amount of DPS. With the Madred's passive and almost 100% critical chance combined with critical damage runes and the Infinity Edge's passive, you will kill very fast.

This guide is based on the first build. I've added a second build that includes more of a standard build for Ashe. You'll deal more damage with the second build, but you won't have as much attack speed, which is very good on Ashe.

Crit Damage Marks/Quints - For the most late-game damage possible.
Mana Regen/Level Seals - Your Q costs mana per hit. With lots of attack speed, you will need mana regen to keep up.
CDR Glyphs - More ults.

21/0/9. This is easily the best mastery tree on Ashe imo. Go offensive for more damage, then utility for time spent dead (you die easy and your team needs you alive as much as possible) and xp.

Double Doran's Blade - Health, life steal, damage. It's the best start overall. When you go back, you should pick up a few health pots too, to give you survivability. You may also need a third Doran's, depending on the game.

Other options-
Brawler's Gloves + 2 Health Pots - You have crit dmg runes, making this a solid start. The health pots make it arguably better than Doran's Blade.

Boots of Speed + 3 Health Pots - Good for speed and the health pots. This is a good start for 2v2 laning.

Flash/Teleport

- Flash can save your life in certain situations.

- Teleport is great for laning early game, pushing mid-late game, and getting to team fights quickly. There's also a trick where you can fire your ult and teleport near where it's going to hit, to get the maximum effectiveness from it.

Other options - Ghost would definitely be by third choice for Ashe and Heal would be my fourth. Other lesser options include Ignite, Exhaust, Cleanse, and Clarity. I wouldn't get Ignite on her, since she should already be killing fast. Exhaust isn't too good, since you have a built-in slow. Cleanse can be ok, but your tanks should be keeping the cc away from you. Clarity is only good if you really use a lot of mana, it's normally a waste of a spell.

Where you lane should depend on who the other team has. Ashe is a great middle against other ranged dps, but DO NOT try to lane her against a mage with strong burst such as Brand or Le Blanc. She's typically best laning bot with a support.

-> You should pretty much always get Boots of Swiftness on Ashe. The extra speed is just really good on her. Another possible choice would be Berserker's Greaves.

-> Infinity Edge is a standard start for Ashe and a must-have on any critical chance build.

-> Phantom Dancer is an ideal item for Ashe. It gives you movement speed and attack speed, which is perfect for chasing/slowing with your Q. It also gives you critical chance, so you can use all that critical damage.

-> Stark's Fervor gives attack speed, life steal, health regen. It's all very good on Ashe. I prefer this to The Bloodthirster just because attack speed works well with Bloodrazor and your Q. If your team lacks AD champs who can benefit from its life steal for your whole team or if its pretty easy for you to stay alive and keep Bloodthirster's stacks, you can choose to get a Bloodthirster instead.

-> Madred's Bloodrazor's passive is great on any attack speed build. It also gives you some extra damage and attack speed.

These are some items you can replace your Madred's with. You could also choose to keep the Madred's and remove the Phantom Dancer instead.

- Banshee's Veil is great for the passive. It also gives extra health and mana, both are good on Ashe

- Trinity Forces gives you a little of everything, it's similar to a Phantom Dancer but gives less damage and some health and mana.

- The Bloodthirster is great if you're doing really well. It'll keep you alive longer with life steal and you won't lose your stacks as often when you aren't dying.

- The Black Cleaver is an amazing item with attack speed builds. The armor penetration is great. It's arguably better than getting another Phantom Dancer.

- Along with Madred's, Last Whisper can make you a real rank-killer. If the other team is tanky, go ahead and get it.

- Sword of the Divine is only to be used to counter dodge champs like Udyr and Jax. If they're being a pain, this item can help a lot.

If you get a Phantom Dancer as your final item, you can sell your boots and buy a Trinity Force. This will only slow you down a little bit and it will make your stats much stronger. But, if you need the extra movement speed, do not sell your boots.

Pros-
More attack speed for your Q.
You have a mixture of AD and AP, thanks to the Madred's Bloodrazor. So, you can't be countered as easily with armor.
Strong late game damage, with high critical chance/damage.
Lots of movement speed for maneuvering, escaping, and chasing.

Cons-
Less damage to buildings, since you can't deal critical strikes to them.
Low early game damage, due to taking crit dmg runes instead of armor penetration or attack speed.
Low attack damage for your W. So, it will be fairly weak with this build.
You use your mana quickly with attack speed + Q spamming.

Remember to use your ult frequently. It's ok if you miss with it. An Ashe that doesn't miss ults isn't using them enough.

Don't farm too much with your W. This can eat up your mana and make you less effective in team fights. Also, don't push with it early. It's best used to farm big waves of minions and to slow enemies.

Remember to use E. Use your E frequently. It's an awesome scouting spell and is generally quite underrated. It also has no mana cost, so spam it!

Stay in the back during team fights. You are squishy. This means you should be the last to join team fights and the first to retreat.

Ashe can chase very well with lots of movement speed and attack speed, but be careful not to chase too far since you are very squishy.