Focus will allow you to land an almost guaranteed critical hit on your first shot of the game. It is best used on a champion instead of a minion. This shot can be followed up / preceded by a Volley for additional damage which can give you the edge in the first fights of the game.
Volley has a very large cone and decent damage early/mid game. Use this to your advantage by positioning yourself to last hit minions and harass the enemy champions with it. However, avoid spamming it early game as you will quickly run out of mana due to Ashe's relatively small mana pool.
Volley diminishes quickly in the late game; however, it still provides a great deal of utility. Volley can slow a great majority of the enemy team, can still be used between autoattacks, hit enemy chasing/retreating in bushes, and more importantly, Volley can pop Banshee's Veils.
When facing melee champions, it is highly advisable for Ashe to 'kite' her opponents via her Frost Shot. Kiting is a tactic which involves constantly backing up and firing intermittently, preventing any melee champions from ever reaching her by constantly slowing them and keeping her distance.
Keep in mind that champions with dash abilities can counter this tactic though once they dash by being able to kite them after their dash allows you to kite even if you get caught.
If you are having mana problems then alternating Frost Shot so it only activates every 2nd attack might help conserve mana while constantly applying the slow.
The high damage of Volley makes it the best skill to start with.
Use Hawkshot to check the nearby jungle for enemies that may be attempting to gank you. It is also useful to check if the enemy is fighting the Dragon or Baron Nashor from a distance.
If your team is engaging either of those monsters, Hawkshot will give you advance notice of enemy approach, but also inform them of your location.
You can use Enchanted Crystal Arrow to help your allies from another lane. If your allies have the advantage, shoot it further up their enemies' lane, and if not, aim further down your allies' lane. This can give your allies the opportunity to strike a killing blow or make a getaway. However keep in mind that there is a low chance you'll hit them and you lose a lot of lane control if your opponent knows it's on cooldown.
Enchanted Crystal Arrow is one of the best initiators in the game, able to stun an enemy (preferably someone squishy) from a distance.
Enchanted Crystal Arrow is also a great skill for ganking. A well aimed arrow can stun the target long enough for you or your jungler to apply their CC as well. Furthermore, Ashe's passive usually guarentees a critical hit if she has been traveling between lanes or not have been pushing the lane for a while.
However, it should be used with caution; Enchanted Crystal Arrow may entice your team to rashly dive onto the enemy character, and headlong into a bad situation. This may result in trading the lives of your whole team for one champion.
Enchanted Crystal Arrow is also a great skill when your opponents are losing the match and are running/escaping. Using it at the right moment can slow the whole team down, grabbing yourself an ace.
When shooting Enchanted Crystal Arrowtowards another lane ping the area it will hit. This will alert your teammates that you have shot your ultimate.
Don't be afraid to use Enchanted Crystal Arrow to escape, however be aware that the duration of the stun is based upon how far the arrow has traveled before impact.
Try to fire Enchanted Crystal Arrow in the same direction enemies are moving, so it is more likely to land a hit. It has a surprisingly large hitbox.
Ashe is one of the weakest 1v1 characters in the game when she decides to stand and fight. Assuming your opponent is as farmed as you are, Ashe is outdamaged by nearly every other ranged AD character, quickly assasinated by nukers/bruisers if caught out of position, and heavily CC'd by tanks that she takes a long time to kill. Although she is considered by many to be one of the "easiest" characters to pick up and play, Ashe is also one of the most difficult characters to master.
However, her strength heavily relies on her ability to kite enemies and punish enemies out of position in team fights with her slow.
It's often best to wait until your allies have engaged the enemy and attack while their focus is elsewhere.
Ashe's true strength shines in teams with tanky characters that can coerce enemy focus and protect her, or perhaps a support that easily peels for her.
Banshee's Veil is extremely good when fighting enemies with strong crowd control. It grants her far more durability from her natural squishiness.
Building Ashe as support is not innefective as she does have a very low damage output. Builiding auras and cool down reduction is an extremely effective way to play her. With her perma-slow, cone slow, vision, AMAZING stun, and requirement to be in the back during a team fight, she can do just fine supporting her team.
Because of her low health, buying an Ionic Spark can greatly improve your chances of surviving and also grant you a large amount of attack speed and another source of damage.
Another similar item is a Wit's End. This is a better choice if most of your enemies are mages.