Welcome to my Kassadin build here on Mobafire, this build works toward Kassa's epic burst in the late game, turning the game to a 5 v 4 since you can burst a squishy down in 3 casts.

Kassadin himself is an excellent laner, he can refresh his mana by autohitting creeps, he can harass without expecting counter harass bcs of silence, and when he turns lvl 6 he becomes one of the best towerdivers/gankers/bullys in the game, Riftwalk to the enemy champ, Null Sphere and Force Pulse him, rinse and repeat.
If he gets low, repeat that combo and add Ignite

now to my skill order, You see that i max Null Sphere first for the Harass and the DMG, Force Pulse is maxed second for that AoE slow and dmg, but i pick a point in Nether Blade at lvl 4, I do this bcs i can charge up my Force Pulse with it and I can recharge my mana easily by attacking creeps/champs.
Ofc i pick Riftwalk whenever possible.

Doran's Ring is an awesome starting item due to AP, MP5 and HP. I pick two of these early on to increase my amazing lane power.

Boots many of your opponents may be already tired of that "Balls to you!" spell that deals dmg and silences them, so they might retreat when they see you come closer, thats why i pick them after my first Doran's so you can still catch fleeing enemies with a Null Sphere.

Tear of the Godess I tried to skip it one game, it did NOT work out, not even a bit, you just need that extra mana to pull of your combo several times.

Sorcerer's Shoes obvious choice, mpen aids way more than extra speed or cdr would.(Core item)

Rabadon's Deathcap as soon as you get this item you should be at least lvl 13, so your Force Pulse and Null Sphere are maxed out by now, which means you can go and Gank or just kill the squishy in your lane all the time. Some harder champs may take some harass first, but Carries and squishy AP's fall to your combo very quickly.(Core Item)

Archangel's Staff Mana/AP/MP5, epic, get it.(Core)

Abyssal Mask AP, Mpen, and That awesome Aura that assists other Magic dmg dealers in your team, aswell as yourself as you are always close to the enemy.(Core)

Zhonya's Hourglass the active into a Flashed Riftwalk lets you escape any ganks. The AP and Armor are pure sweetness.(Core)

Void Staff if the enemy team is building against you(Heavy MResist) get this, if not get another Archangel's Staff or Rylai's Crystal Scepter(optional/core if they build against you)

however, if the enemy team is doing well in killing you, try to get a Banshee's Veil or Quicksilver Sash if there are well doing APs with alot of cc.

If the enemy team is full of stones(I like to call low skilled players that feed alot stones.) pick a Mejai's Soulstealer early on, makes you unstoppable through mid game, making you a huge threat to anyone Late game.

Runes:
Reds: Greater Mark of Magic Penetration Mpen which almost equals 30 with your Sorcerer's Shoes
Yellows: Greater Seal of Scaling Ability Power since you build towards Survivability and Mana with your early game items you focus on AP with runes, and since kassa is quite weak till lvl 6 and up, you rly want to get scaling AP runes.
Blues: Greater Glyph of Scaling Ability Power read above.
Quints: Greater Quintessence of Scaling Ability Power read above.

Redone Masteries: 21/0/9 since all those offensive abilities compliment kassadin very well, especially like the last talent in the offensive tree, ofc the AP is great too. Then to the Utility tree: Improved Flash ofc, reduced death time, movespeed. Now the last point is odd, pick whatever you like, 1% spellvamp looks like a total waste. extra gold = rather good choice, Increased buff duration = quite good, wards? nope. Empowered Recall, i tend to like this, especially when ganking often a quick recall saves a lot of time which makes up for lost gold from the G per 5 mastery and.. well just look at it this way: You'll be on the lane 1 second earlier than ur enemy. Except if they skilled it too^^

Summoner Spells:
Flash into Riftwalk saves your life or secures kills.
Ignite is just great against strong healers/selfhealers or to add that little extra damage to net you a kill. Also great vs Well doing tanks since 500 true dmg are a sure thing.
(this does not mean you should focus tanks, rush in and out of battles if your combo is up killing healers/carries/or casters. Slow down running enemies with Riftwalk and Force Pulse.)

Harass your lane opponent or opponents with Null Sphere kick channeled spells with Null Sphere (makes Kata and Nunu rage since August 7th 2009)(kassa's release date in the US)
When they overextend and your Force Pulse is ready, hit both(on a duo lane) or that single hero with it and smack Null Sphere on one of those two(on a duo lane) or again on the opposing hero. Autohit creeps to regain mana with Nether Blade try to last hit at your best, but full mana to deny the farm of the enemies with your skills is somehow way more important^^

Mid Game: Your full power should be reached by then, Riftwalk lvl 2, Null Sphere maxed Force Pulse Maxed, roam around and look for kills, ask your jungler(if you have one) if you may get the blue, if not try to get the enemy blue, but don't go alone if you don't feel safe. Use Nether Blade whenever it's off cooldown to kill some jungle creeps/normal creeps and to charge your force pulse. Focus Squishies in those small teamfights, try to be in every teamfight since you can really turn everything around with a pinpoint silence and AoE slow.

Late Game: Pretty much the same as Mid game, except that you stay with your team, however if you see someone farming on top/bot lane and all the other enemies are mid, rush top/bot kill that champ and tell your team to start a fight if you were succesful, by the time the fight starts you're already on your way back to kill another squishy with your burst combo, slow runners with Force Pulse and your team should be able to finish the last 3 enemies with your help.

Pros: Amazing Dmg output.
Very Mobile.
Got alot of CC.
Little Flash at lvl 6.
Best Kiter ingame.
Good Harasser.
Takes reduced magic damage.
Close to Invulnerable with Riftwalk
One of the Best towerdivers.

Cons: Squishy early on.
Weak early on.(fades as soon as you max Null Sphere
Mana Hungry making him Tear or Blue dependent, best to have both :D
If the enemy team is full of tanks his effectiveness falls flat.
Lategame carries are able to kill you if you don't approach carefully.
Needs alot of Awareness to be played at his best.

Riftwalk is a very versatile spell, you may steal a low life creepwave with it, jump over walls to steal Baron/Dragon, Chase and Escape and much more. But the thing you might use it for the most is Escaping or Chasing, the power to negate the enemy champions flash by riftwalking towards him is very powerful, since you got a flash too, you are a strong chaser and escaper.

Jumping over Walls to escape your enemies is one of your best bets since no one should be able to chase you properly, and if a single squishy does, without his team to back him up(communication problems ftw) wait in a brush, burst him/her down and then retreat.

Example: I was lvl 18, attempting to kill Dragon, Three of the enemy team show up, Master Yi Tristana Brand (all lvl 18) I Riftwalk out towards our jungle, Our dragon ward allows me to see Brand and Yi finishing up dragon whilst Tristana is following me with Rocket Jump i wait in a brush, kill her Instantly with Null Sphere Force Pulse and Riftwalk into Ignite After the enemy carry was gone, we started a teamfight with me focusing and killing brand, whilst my team mopped up the rest of the enemies.

Having a Tank/Support warding Key locations may get you some surprise kills on stupid or overconfident enemies ;)

I hope you enjoyed this build alot.
I wish you good luck on the Fields of Justice and a LOT of fun playing Kassadin

Peace out :)