Not Updated For Current Season
(Passive) Void Stone - This ability is a bit of a disappointment, but are still isn't to bad. Kassadin takes 15% reduced damage from magic based attacks and converts it into attack speed. If this converted it into attack damage, I think it would be better, seeing that Kassadin's hits are not that hard.
Null Sphere - Your standard ranged nuke, with a silence. I only put two points in the first few levels, because if you're using this correctly, you're trying to last hit minions and harassing enemy champs in the beginning and if you use it this way while farming it will eat your mana. Later it will become a strong slap to the face to enemies who are close to death.
Nether Blade - Again, another disappointment, though the passive and active are both great I don't see it being useful for this particular champion. I think it would be great for almost any other melee based champion. I get one point in early levels so that it may help you gain an additional charge for your Force Pulse whenever your CD is up.
Force Pulse - This is what you want to use whenever you gank. This ability hits and hits hard in a large cone in front of Kassadin, not to mention the nice slow you pile on top of it. The downfall is that to use it, you or anyone near you (Including enemy champs) must use 6 abilities before being able to slam them with this bad boy.
Riftwalk - This is the entire reason to play Kassidin. Riftwalk allows you to teleport to a targeted location, with small AOE damage, AND with only a 4 second CD in it's latest level! With great power comes great responsibility however, with each teleport used (in each port) within 7 seconds costs 100 more mana, and does an additional 100 damage.
Your skill combo should be this...
Riftwalk>Force Pulse>Null Sphere
If need be throw an ignite on them
1. Summoner Spells
Great for ganking.
Is great for when you're on the chase, but isn't necessary as you have a built in slow, but if you do in fact take it, you should take a point from Deadliness and throw it in Cripple.
Good for early game farming.
Kassadin is manastaved, which calls for him to almost rely on the mana saving effects of Clarity
It can definitely help with ganking if you port in and assault someone who is either alone or low on health.
People will often try to CC you on account of your ability to vanish away.
Good for throwing on someone who is close to death on the run.
I choose Ignite and Clarity because I see them as the most useful for Kassadin.
Avoid taking any and all damage from champions and farm minions as much as possible. Harass with Null Sphere or try and last hit minions with it. But you are squishy and week, so do your best not to get hit.
After level six you're now the king-o-ganks. Riftwalk in, slow, then nuke with Null Sphere. Always and I mean ALWAYS have an exit strategy just in case things get hairy. Also never ever jump into a group of enemies, try and take the ones who are at least close to half health.
Your slow and nuke should be absolutely devastating to enemy opponents, if you're going to go into the enemy base never go alone as you are still squishy-ish. If you're confident in your abilities and you're not dealing with much CC you can try and pick off your enemies in a group one by one.