This guide will explain in depth on how to play and build SOLO TOP AP Master Yi. Please note that AP Yi should really not be played in any sort of high ELO games, as it doesn't near the viability against Jungle Yi.

Pros

Good harass from early to late game
Controls lane easily
Great burst damage
Great heal which tanks
Great farming capabilities
Click Q and watch an enemy disappear off the screen

Cons

CC rapes him
When Alpha-strike is on cooldown, you deal close to 0 damage
When Meditate is on cooldown, you are extremely squishy (also when stunned out of Meditate)

You should be aiming to have blue buff all game except for early if your Jungler needs it, but after the early jungling stages, either get your own or your enemies blue buff, it makes a massive difference. Remember to always blue elixir when possible, 40% CDR makes you a boss.

Flat AP bonuses are extremely good as AP scales 1 for Alpha-strike and helps with Meditate 0.3

Flat AP Quints x 3
AP/lvl Seals x 9
AP/lvl Glyphs x 9
Magic Pen Marks x 9

This is the optimal build to deal as much damage as AP Yi. There are other alternatives such as Magic Pen Quints for a slightly advantaged mid-late game, it won't be much of a bonus. Also you can opt for flat AP runes, however this isn't optimal as AP/lvl runes equal out to flat AP runes at lvl6, meaning flat AP runes are only useful if you intendt of killing/harassing/healing a lot before lvl6(?) sounds dumb to me. Mana regen/lvl seals and CDR glyphs can also be used. AP runes however benefit the most if you wish to melt opponents from beginning to end game.

Standard AP caster setup.

Standard 9/0/21

Grabbing Teleport and Flash mastery (Ignite is only situational for an opposite team of healers such as; Mundo, Fiddle, Warwick etc)

Starter Items

Doran's Ring

This gives a slight edge on HP, allows you to harass with Q and heal with W while giving you a minimal AP boost.

First/Fast Return Items

Doran's Ring x 2
Sorcerer Boots

The reasoning behind grabbing an extra two Doran's Ring is because it will let you farm and sustain a lot longer in lane as it allows you to farm/harass more and gives you survivability with that added total of 300 hp. I highly suggest not skipping the extra two Doran's Rings as it really is what keeps you in lane. I really don't see why you would opt away from this unless you were melting and raping extremely hard for you to get a quick mejais. Note that this still won't give you mp regen or health; the core to sustaining and farming lane.

You want to level up Q and W as you go. Getting a point into E early is an option, as it grants you a passive +15 AD aswell as +30 AD on active, it really is up to you.

R > Q > W > E

Alpha Strike

Farm minions and kill enemy champions
Dodge incoming attacks including CC and big nukes

Dodging with Alpha Strike is fairly simple, timing it with an incoming attack will work this way; say Sion stuns you, the incoming projectile can be dodged by Alpha-striking onto a nearby creep/champion while the stun is still mid-air. Note that the stun will still hit, just that the duration will prolong during your Alpha strike.
For example: Say your Alpha-strike lasts for 1second and Sion's stun is 2seconds, if timed correctly you can come out of Alpha-strike with only a 1second stun remaining.

Meditate

Wins fights
Lets you live
Trolls enemey team
You get owned if you are CC'd

Meditate can be used to bait enemy teams and win fights for your whole team and win the game. Make sure you know which CCs are up and ready from your enemy team, your aim is to get meditate down as soon as all CCs have been used as being stunned during meditate will cost you your life. You can pretty much tank a whole team beating a way on you with one meditate from start to end.
Note that meditate is extremely useful against skills such as Karthus' ult and Caitlyn's ult just as an example of the various few. Meditating as soon as you them ulting will increase your armour/magic resist by 300 and begin your insane heal (from your AP) and let you survive EVERY time.

Wuju Style

Begin fight > Click E

Pretty straight forward.

Highlander

Disables all slow effects including Exhaust
Makes you run extremely fast
Makes you attack like a boss

Needless to say, pretty straight forward and a great skill to make Master Yi a number one candidate for backdooring.

Teleport and Flash

Teleport

Allows you to get to lane quickly
Allows you mobility to gank opposite lanes
Allows you mobility to backdoor

This is mainly because you are soloing top and really need to get in and out of lane to buy items and heal up. Ignite can take over Teleport if you choose not to solo top lane.

Flash

Like a boss

Laning and Goals

Although AP Yi is deadly from start to end, a farmed AP Yi is five times as deadly. Spend your first 20 minutes farming your lane as hard as you can with Alpha-strike and ganking near-guaranteed kills time to time (preferably not across the map). Push towers (backdoor if needed) as much as you can with Wuju Style and Highlander.

Fighting

Get in there use Alpha-strike and chase only if you know you are safe/guaranteed a kill (which you almost always should be). Don't chase too deep especially without highlander or meditate as you won't be able to get away unless using a well-timed flash. The drill is to get in Q > Kill > GTFO. Don't try and hero team fights and stay in there attacking, as you really do close to 0 damage without Alpha-Strike.