Ashe isn't the normal AD Carry you see in SoloQ. She's more of a supportive carry, considering her kit and low damage during early game.
Don't be worried if you aren't getting many kills, focus on farming and avoid dying and you are set to carry late game.

Ashe struggles during early game
Hide your weaknesses.

I, for one, prefer to early harass with my AA and W in order to:
-Push the lane.
-Harass the enemy carry/support.
-Make the enemy carry lose CS under the tower.
-Call their jungler in order to let top and mid have more freedom.

Of course, this doesn't always happen and sometimes you'll even be zoned from farming; but don't worry as I've been saying, you are a supportive carry. Focus on not dying (meaning, giving kills to the enemy ad carry) and farm. Even if the enemy carry has more 30 cs than you do, you'll be more useful due to your kit and utility.

Tip: Once you reach lvl 2 harass like this: Auto attack with your Q followed up by your W. If your support is tuned in, this can make you win the lane.

Looking to group up for objectives
During this phase you'll need to start being more cautious.

Things to avoid:
-Moving between camps without proper vision.
-Getting greedy and following a enemy to their jungle with no vision.
-Positioning in the front line.
What to do:
-Safely farm between camps.
-Stay on the back of your team.
-Initiate on a off-position carry with your arrow

Teamfighting
The time has come. You were dancing around between drake and the enemy team decided to contest it. It's your time to shine.
Aim to hit your arrow to one of their carries. You don't need to say a word in team chat, that itself is a big "I got one of their carries, follow up team" and your initiator will immediately begin the team fight.
During the team fight be sure to be properly positioned and constantly use your volley (W).

Auto attacking:
-Always auto attack what's closest to you. You are a Attack Damage Carry, meaning you have to put as much damage as you can into something. You also can't die early on, because that means your team will miss some of the most damage output.
-Make sure your Q (slow) is activated. Helps in kitting.

Step up as a playmaker
Arrow to win.

Now you are off with your team, fighting for inner towers/barons. Any mistake will cause a loss, and you are the best champion, in the entire game, that can punish as hard as a guaranteed loss to who ever gets caught.
Ask for your support to extensively ward the enemy jungle (if you are the one targeting the enemy's inhib) or your own jungle (if you are being pushed back) - do help if you have a spare 75 gold and free slot: but at this point you shouldn't be helping in warding.
Your objective is simple: Correct positioning and using your arrow to whoever is out of position (yes, that means even if it's a tanky jungler - during late game respawn timers are high and going in a 4v5 is almost celebrating the win).

What if they're a organised team?
Rarely it happens, but sometimes in SoloQ a team can be pretty solid in terms of positioning and protecting their carries.
In that case:
-Look to arrow who ever can hit you.
-Do as most damage as you can to people closest to you.
-Volley in order to deny some movement speed to everyone who gets caught in it.

Ashe's arrow.
That alone can change a game. Imagine you are at the 45 minutes mark and both of the teams are doing the mexican stance near baron - this is when it's up to you to decide the game. Not some jungler/mid/top initiation, but you and your arrow.
Try to get a arrow on one of their carries. If you single him out right at the beginning of the fight, it'll be a 4v5. Of course, sometimes it's hard to get that arrow to hit because their carries are correctly positioned - but this is soloQ and people have no real communication other than chatting and watching their team mates movements which will cause someone to be out of position for a couple of seconds and that's when your arrow can - and will - make the game turn to your favor.

Simply train two basic things:
-Avoid dying for that extra cs.
-Put your pride aside - sometimes you lose the lane.
Understand that you are a supportive carry till late game because, until then, and unless you are fed, your damage output is very low. You'll be setting up kills with your slows to your fellow team mates.
Focus on safely farming and bringing your playmaking value to teamfights.

Alistar-One of my favorites. A good alistar will provide you so much safety that you'll be untouched. The minor heals help alot in lane.
Bard-Very versatile. His shrines are very good (especially early on for sustain) and allow you to have a good laning phase to carry late game.
Braum-Very much like Alistar, it will help you with a great utility both in offense and defense.
Janna-My favorite. No one can touch you, you'll get a AD boost shield and peeled for.
Karma-The poke she brings and the shield can keep you safe.
Lulu-Poke+Safety for you? One of the best.
Lux-Double binds and a shield.
Morgana-One of the best supports at the moment for both defensive and offensive options.She can be VERY useful at level 6, when she gets ulti to compliment yours.
Nami-Sustained heal along with a heavy CC at level 6 can guarantee you a kill.
Sona- One of my favorites. At level 6 it's just absurd what you can do with her.
Soraka-Very passive, allows you to farm the entire game.
Zyra-Perfect for harassing. Plants and frosty arrows are painful to watch.
Blitzcrank-At level 6 you can lock the carry that will get pulled.
Leona-Secured lockdown at level 6. If Leona gets her ulti to stun the AD Carry, it's a kill.
Taric-He can burst the enemy support by himself at level 6.
Thresh- Once the cage is activated, there's no escape with the amount of cc.