Ashe is a very unique Marksman in that she is extremely vulnerable to hard gap closers but has the potential to slow the entire team and not let anyone escape her damage because of Frostshot. It's important to be patient with her and not take unnecessary risks where people can exploit her lack of mobility. Wait for the right moment and hit their carry with a well timed Enchanted Crystal Arrow and swing the game greatly in your favor.

Pros:
Permanent Slowing/AoE Slowing
Enemies can't escape damage
Global stun
Synergy with crit
Scouting ability

Cons:
Lack of mobility
Low burst damage without core items
Vulnerable to enemy engages

Getting Ghost AND Flash is very useful for Ashe, since it solves her biggest weakness which is mobility. Ghost is good for chasing people down and taking them down with Frostshots and also for getting away. Flash can get you out of a lot of sticky situations or it can secure a kill. Try to prioritize using Ghost if possible because it is on a shorter cooldown. Also getting distortion on your boots is a very nice bonus.

Frostshot: This ability allows Ashe to slow a target until she runs out of mana (more of a concern early on). Learning to toggle this spell on and off properly is one of Ashes harder mechanics but since you dont get punished severely for not doing it perfectly it's nothing to worry about.

Volley: Ashes only consistent damaging ability. Use this to poke at your opponents and to do AoE slows. Be careful to not put yourself in danger while trying to land this spell.

Hawkshot: Should be used to check areas before you or your team crosses into unknown territory. Also use this to not allow enemies to escape by going into unwarded brush.

Enchanted Crystal Arrow: The ultimate ability is the crux of Ashes power, use it to initiate fights, to pick off people trying to escape, make miracles happen across the map, or to defend yourself from someone who got through to you and will otherwise kill you (catching people with it once they have committed to tower aggro can get a kill)

The key here is to max Volley first then try to max as much of Hawkshot as possible for the gold generation until the game transitions into fighting, at this point max Frostshot so your slows are more impactful.

During the laning phase you should try to neutralize the lane. This means push only as hard as the opponent is pushing. Ashe is inherently vulnerable so you don't want to be pushed up without excellent vision control. The longer you wait to use auto attacks the more her passive stacks up which should be used to poke along with volley. Also Ashe is very good in a bot lane skirmish so you want them to be pushed and vulnerable so they are risking getting slowed and stunned in an engagement. However you don't want them to build up momentum with minions to where they can collapse in on you under tower.

Remember the general strategy for Ashe is passivity, take your time don't try to force things to happen and surprise people with your Arrow.

Ashe works best when she has allies around to help her. Let the enemy commit to fighting your allies before going full on. Meanwhile try to poke them with Volley but don't get greedy with it and let them engage on you.

Infinity Edge and Phantom Dancer are the two main items which let Ashe take off as a serious damage threat.