I first played kassadin a a few weeks ago, that's the day I found out I've found my favourite champion. Kassadin is just all around a great champion, He can escape ganks easily, gank easily, great in team fights (silence) and has a great AoE slow. I play kassadin more aggressively than most but it's paid off if you look at my recent match history. Itemwise I tend to get to my void staff in most games I play, most of the games I play I get pretty fed going 15/0, 24/2 and 15/5.

Teleport : Force pulse is a great way to kill minion waves, utilize it as much as you can. Teleport is also a great way to get to lane fast, teleport is just a great spell overall. You can teleport to turrets to save them and just ... have fun with teleport ;)

Cleanse : Cleanse is a GREAT spell for kassadin, if used properly you ... just can't die. You can run into 5 people in the jungle and get out alive with a few scratches on you. I'll explain why cleanse is so useful later on as well.

Kassadin is a great mid against casters, such as swain, TF (sometimes) and other champions. He is also a great side laner. You just level up your null sphere/force pulse and harass/last hit minions. When you get your ultimate use it when you think appropriate to Riftwalk in/Null sphere/Force Pulse and whack them a few times. Kassadin is also a great ganker, Riftwalk is a skill that is great for ganking, utlize it whenever you can. I tend to get my Mejai after my level 1 boots and than build them into sorc. treads.

By now you should be at a few stacks, just keep on running around ganking whenever you can, keeping your turrets safe and just farming when theres no one to gank. By late game, if played properly, you should be an unstoppable force. You'll be able to one shot casters, half health those tanky dps'rs and be unkillable. People will fear you and run away from you whenever they can. Even if theres 3 of them and 1 of you, they'll be scared shi*less. :) (Keeping Mejai stacks is very important!)

Teamfights, Kassadin is great in teamfights, although he may not fully be there he's helpful. Once a teamfight if initiated by your tank or the opposing tank your job is to kill the squishies. You rift walk around silencing/AoE slowing them and just raping them in general. Kassadin is also a great chaser, only chase after champions if you know people have your back otherwise you may be killed.

What you want to do in order to nuke successfully is rarely force pulse minions unless there is a huge wave of them. Keep force pulse up for those times you really need it. I tend to rift walk in, null sphere and than force pulse, keep whacking them until null sphere is up again. In team fights force pulse comes up extremely fast, take advantage of that. Nether blade is pretty much a useless skill, I don't even bother using it.

A whole section on Riftwalk, awesome :). Riftwalk is by far one of the greatest ultimates i've ever seen, with its super low cooldown you will be unkillable. If things get sticky, you use cleanse and get the hell out of there. Cleanse is great for escaping, if your stunned you cleanse/riftwalk and bam, you are a safe distance away from the champion(s). DO NOT INITIATE WITH RIFTWALK

I just thought I'd throw this in here, Oh how important map awareness is. I usually play arranged team but when I do play solo my teammates forget to call mia and I get pretty frustrated, me playing Kassadin though, I rarely die. Watch the map, you can easily tell half of the time if they are coming towards your lane. Look at your map, are you pushed up far? and do you see any enemies on the mini map? If the answer is no I'd get the hell out of there.