Ashe can have very strong poke without having to buy many Items while she also offers some good if not always available utility with her Ult and E. By just building mana regeneration and CDR (stats that are very easy to get with runes and cheap Items) and building Liandry's Torment Ashe has amazing poke on her W. While the damage of an individual W might be unimpressive but the fact that it has a 4 seconds base Cooldown (at skilllevel 5, 2.2 seconds CD with 45% CDR) and is very easy to hit and hard to dodge makes the damage rack up very quickly if Ashe can get into range to poke. This poke can easily rival the poke of Vel'Koz Support, the other poke Support. Since the W is so spammable has great range and slows Ashe can also poke very well with it. The fact that Ashe only needs so little Items to get good poke means she can use all additional money and the other Item slots for lots of different things like utility and tank Items but also more damage Items. This gives her a lot more adaptability in her build compared to other long range, high damage Supports like Zyra and Vel'Koz. On the flip-side she doesn’t get as much teamfighting damage as those two although she packs some nice burst in her Ult and her DPS is still higher than that of a lot of utility supports. Overall Ashe is an adaptable support with very good poke and kiteing as well as some nice utility from her Ult and E plus that from utility items you might have bought.

The most important thing that distinguishes Support builds from other builds is, that they have to be very cheap since supports don't get a lot of money. That's why building a standard ADC build on a support is not viable – ADC-builds are expensive. Liandry's on the other hand adds a lot of damage for a single Item to your W even though the stats on it are mediocre. In fact the only Item that can contest Liandry's for bonus-damage-done per W is Mortal Reminder if you count healing prevented as damage done. Don't believe me? Here is some math comparing Mortal Reminder (without grievous wounds) to Liandry's.

Liandry's Torment ticks three times after being applied by W-volley the first two ticks do 4% current health as magic damage since the target is slowed and the last tick does 2% unless an Ally helps you out with their CC. Overall this means that Liandry's adds 10% current health as magic damage per volley as Bonus damage. Now lets assume we're hitting an enemy with 2000 maximum health and 70 magic resist. Most of the time players have higher armor then magic resistance but lets just assume the target has 70 Armor as well. Since we are mostly going to poke we are mostly going to hit still healthy champions so lets assume the enemy is between 50% and 100% maximum health which leaves him at 1500 health on average. Liandries now does 0.1*1500*(70-15)/(100+70-15) = 97 bonus damage. Without Mortal Reminder we'd do (at level 18) 190 base physical damage per volley that's 190*(1-70/170) = 112 after armor. With Mortal Reminder we'd do 240*(1-38.5/138.5)=173 damage after Armor. This means Mortal Reminder adds 61 damage per volley. As enemy health increases this is only going to shift in favor of Liandry's Torment.

Pros:
-Good poke throughout the game
-Good zoning capabilities
-High damage (by poking)
-Safe (deep-)warding with the help of E and W.
-Strong utility from your Ult.
-can Kite really well
-chasing you can come close to the futility of chasing a singed with the right itemization
-very adaptable build (for a high damage support)

Cons:
-Has some lane matchups where you can't do much
-Annoying power-dip while building Liandries
-While you're Ult is on cooldown you can't do much except poke and grant vision
-Weak teamfighting damage (compared to other damage supports)

This build wants to maximize the damage you can do with W-volley while also providing some nice utility. To accomplish this the main stats that are Important are CDR and some manaregen as well as AD. With the core Items we already have 35% CDR (at level 12) so we don't want to buy more than one CDR Items after that if we can avoid it. If you can safely kite the enemy team just go for more Damage at this point. As shown in the calculation at the beginning you already do quite a sizable amount of damage with just basedamage and Liandry's Torment. More importantly building more AD Items doesn't increase your volley damage by much so it's sometimes just better to go for tankiness or utility instead of damage. Building tank allows you to play a little more aggressively and thus get more volleys in whereas the utility items are useful because of the stats they provide to your team.

Core-Items:
For gold generating Items the choice is between Ancient Coin and Spellthief's Edge. Ashe is really good at applying spellthief’s passive but ultimately Nomad's Medallion + Sightstone gives you basically the same stats as Eye of the Watchers for 550 less gold and leaves you with the option to build Talisman of Ascension so it's overall better.
The next two core-items should be fairly obvious as to why they were chosen.
Get these first three Items in whatever order you deem best for the situation.
Next get Liandry's Torment. If you want to know why read the paragraph in the beginning of the guide.

Defensive and Utility Items:

Dead Man's Plate:
This Item is the perfect tank Item for Ashe Support. It gives good tank stats and the bonus movement speed helps her a lot since it makes kiting much easier and allows you to play more aggressive without being punished for it. With this item you can get away with a lot of **** you otherwise couldn't. The constant damage and slow from your W in addition to the added mobility of this Item allow you to shake of almost anyone chasing you and your high range allows you to get into a position where the enemy is encouraged to chase you away or back off. The added mobility also gives you some extra chasing power to help your teammates with catching up to enemies.

Talisman of Ascension:
Stat wise upgrading your Nomads medallion gives you some armor and situational movement speed. The main selling point is the active though.

Banshee's Veil:
The tank item if you just want survivability against magic damage. As long as the shield is up you can position more aggressively to get in more Volleys.

Locket of the Iron Solari:
This gives you CDR and some MR. Go for this if you're team needs the MR more than you do. The active and Aura also contribute to your teamfight presence.

Maw of Malmortius:
A nice Hybrid between Offense and Defense. Good if you have problems with a single magic damage source but can kite the other enemies well.

Mikael's Blessing:
You get this Item for the active, not the stats. But while the stats are not plentiful they are all of use to Ashe support so that certainly helps. Most notably the extra manaregen eliminates pretty much all mana problems you might have had before. The active can be used on yourself so having it of CD allows you to position more aggressive against champions with strong snares or slows like Morgana.

Zz'Rot Portal:
This item allows you to counter a splitpusher or backdoorer by pushing out the wave and giving an early warning on incoming backdoors.

Offensive:

Mortal Reminder:
This Item is very good on Ashe since she can Apply the Grievous wounds consistently to a lot of people with W-volley. The armorpen is also good since W has decent base damage and this Item is the second best Item for damage done per W. If you think it's worth it get executioners calling before finishing Liandries.

Youmuu's Ghostblade:
Gives CDR, AD and armorpen an on top of it attackspeed for a limited amount of time. This item is very good If you want some bonus DPS for teamfights and overall your go to Item if you just want more damage.

Black Cleaver:
Ashe is really good at applying black cleaver stacks. Get it when your team has a lot of physical Damage and the enemy is just stacking armor. It gives you more CDR then you can use so you can change boots after you get this. One thing to note is that your Q enhanced autos apply five stacks of Black Cleaver at once.

Duskblade of Draktharr:
While this Item is not on CD your kill pontential and dueling power rises by a lot. Ult + duskblade-proc is a lot of burst damage that can be used to kill enemies you've softened up with W before (or that got low otherwise). The stats are also all great on Ashe.

What to do with excess money

When to Build ADC (and when not):
Very late into a very long game it can happen that even the support has full build and a lot of money leftover. In that rare situation it might be worth it to sell your support and tank Items and go for an ADC build instead. However the situation where this is possible is very rare and even then doing it will not always be the correct decision. It's probably best when you have a lot (3+) of AD-Items already. In that case it's best to build more AD-ratios (so attackspeed and critchance). The best Items for this are probably Berserker's Greaves, Phantom Dancer, Runaan's Hurricane and Blade of the Ruined King. You are sacrificing your Sightstone and some poke for this though so it better be worth it. When you were building a lot of tank and utility Items it's probably best to just keep your current build and just keep on doing what you've been trying to do the entire game so far. If you have surpassed the CDR cap you can swap boots. The most important thing to take away from this paragraph is that it is only relevant in maybe 1 out of 50 games so it's not worth it building towards the adc build since the game will just before the investment has paid of most of the time.

On Boot Swaps:
If you have to much CDR switching boots is a good idea. You can even swap boots when you don't have full build yet since it is very cheap (470 gold for Mercury's Treads, Berserker's Greaves and Ninja Tabi). There are several options if you want to switch boots: Mercury's Treads and Boots both make your kiting better and allow you to play more aggressively. Which one of those two is better depends on the enemy team. Ninja Tabi are generally a bad choice since you should be able to stay out of autoattack range but it might be strong choice occasionally against very autoattack heavy compositions (but even then it's hardly an auto buy). If you have a lot of AD Items you might consider going for Berserker's Greaves. They add 0.21 attackspeed which translates to 0.21AD physical DPS while autoattacking. They are a good choice If you already have some AD and armorpen Items.

Elixirs:
The blue elixir gives you some nice bonus poke damage and some additional manaregen that is very appreciated. The Elixir of Iron gives you tenacity and tank stats as well as the path of Iron and Increased size. This makes it pretty useful when you have a very tanky build. I usually don't get the red elixir since the blue elixir just adds more useful offensive stats and the lifesteal is pretty much useless with the low autoattack dps of this build. If you want more teamfight damage this late into the game you are better of switching to an ADC-build instead of investing in elixirs.

Skills:

Q: This skill is mostly useless which is why I often don't even put a single point into it until I have to. As support you don't attack minions and thus you can't even build up stacks reliably. There are some situations in which it is of some use though. For one it is an AA-reset which means you can use it to do some bonus damage in long fights (long being you can attack at least 4 times to get all stacks). It also applies 5 Black Cleaver stacks per enhanced Auto.

W: You're bread and butter. The entire build revolves around this skill. Try to hit as many enemies with it as possible. Use it to slow down chasing enemies. Use it to chase down enemies. Use it to check bushes or check for invisible champions (the projectiles disappear once they hit something). But most importantly use it as often as possible to slowly poke away the enemies healthbars. It's important that you get a feel for the range of this skill. Most of the time you want to shoot the arrows in a way that they hit the enemy at or close to maximum range. Doing this allows you to kite them very well. Due to the range of this skill you can often still contribute to a fight when you are very low. Just make sure to that the enemy high mobility assassins or long range champions can't kill you for free.

E: This skill is often under appreciated. You can use it to do several valuable things. It allows you to place deeps wards safely, it allows you to chase down enemies that escaped into the jungle, it allows you to check whether you can pounce on an enemy champion or if his buddies are right behind him. You can also use it as a tool to stop enemies form juking or escaping by going into bushes. It can be used as a makeshift ward while doing an objective as a team to go into an upcoming fight with all the information needed for good targeting of your skills and good positioning. Or you can use it to assist someone in pushing down a tower (or taking another objective) by making sure it's safe.

R: Not much to say about this skill. If you are new to Ashe don't over think aiming the arrow
just trust your intuition and try aiming for shorter range arrows first before doing the advanced stuff. If you are looking for a more in depth guide on aiming this skill look at some other Ashe guides, this skill is basically used in the same way as an Ashe ADC would use it.

Earlygame:
Try to harass the enemy with Autos and Volley. Play as aggressively as possible, the only thing you can do to support your ADC is to harass and pressure the opposing laners and you are very good at that. Scout for their jungler or setup deepwards with E. If they have a big bully as support (like Leona or Nautilus) play a bit more defensive and only harass when you get an opportunity where it's safe. Once you get your Ult you might be able to get a pick.

Midgame:
Poke, Zone and Kite with Volley. Go into autoattack range only when it's safe to do so. Think of yourself more as a mage than a marksman. Don't forget to ward. Using E + W allows you to place even deepwards very safely. If you don’t have Liandries yet you probably can’t poke to well at this stage so just focus mostly on vision and your ult. You still can do some damage with autos and volley though.

Lategame:
Do more of the same stuff that you'd do in the midgame.

Lanematchups:

Allied ADC:
Ashe generally does well with an ADC with a strong earlygame but she can work pretty well with an average ADC as well. Just don't play Ashe Support when you're ADC wants to play Kog'Maw.

Notable Synergies:
Jhin: Besides just being a strong earlygame ADC Jhin can really profit a lot from the things Ashe can offer. She constantly damages and slows enemies with W which makes them easy targets for his snare. His Ult also profits a lot from Ashes E and R.


Opposing Support:
Ashe support struggles against CC and damage heavy supports like Leona and Nautilus. She has a pretty good or neutral matchups against most other supports. Soraka can be a problem though especially since you are a poke champion throughout the whole game and she counters that pretty well. Velkoz is also a problem since he just outdamages you in lane.

When playing this build it will probably happen occasionally that you get flamed by a teammate for the pick. It is usually best to just ignore it or if you have trouble ignoring it to mute the player. You can't get reported for playing an off-meta build so don't worry about it. If you want to play Ashe support in draft don't prepick her since people like to ban prepicks they deem troll. Sometimes ADCs assume that you will steal their farm so it is sometimes helpful to assure them that you wont steal farm.