Not gonna lie, I've always played Kassadin as straight AP untill I heard of actually utalizing his passive. First game I played with this build I absolutely DESTROYED a 3v3 game, and then a few 5v5's after that. With the right team comp and the right amount of skill, you've got yourself a mighty force in your hands.

for the items, as seen above, you start out with a few items to get your attack speed going, also the malady for extra dps. wit's end is really vital to this build, because it allows you to wreck any mage on the other team, while boosting your attack speed greatly in any fight. with trinity force, its just a little bit of everything, attack speed, ap/mana (and the damage from sheen), along with some health/damage and a slow. Over all a good pick. Then we get on to late game items, such as starks, rylais, even a Deathcap. But really, the game shouldnt go on this long if you dominate. seeing as in 3s the game can be over before trinity force is complete.

With this build, Kassadin really doesnt need the small burst from his Q, though the silence will help him wreck mages. But what you really want to focus on is his E, because the slow will ensure you many a kill and will also help you farm large amounts of minions mid to late game. its really a big deal in 5v5 teamfights too because kassadin doesnt really have any other form of AOE, unless you build Tiamat, which I dont recommend. (trolololololo)
Other builds may suggest that you max your W for more ARP, or Armor Penetration. This is wrong. The small amount of armor penetration it gives you wont compensate for the massive AP damage you do even without going straight AP, and all the W does for you anyways is get you more mana back with which you cant do anything important without ranking up your other spells.

For summoner spells I use Ghost Ignite, Though you can really use anything short of the already known "I WANT YOU TO QUEUE DODGE REALLY BAD" spells. You know, Rally/Revive/Heal. Basically Teleport, Exhaust, Ghost, and Ignite are going to be your friends as Attack speed Kass. (flash really isnt much of a help as kass, seeing as your ultimate is already a great 2 second cd flash...) Clairvoyance.... Leave that to the soraka's and battle janaa's. As far as Clarity, You have your W, just kill creeps and stay in your lane.

Kassadin is a great farmer, especially with this extra melee speed boost. His great maneuverability make him able to sneak in the last hit now and again, along with the early game Q's to secure the gold. Late game, Kass can just E down a full minion wave, or just the casters. Along with the kills you'll be raking in, Money shouldnt be an issue, but if you have any trouble, starks or any form of lifesteal will make you an excelent jungler.