This is Mainly a build but I will throw in a tips and tricks on how to succeed with Kassadin.
While lanning with Kassadin, the key is to NOT die before LEVEL 6, if your not able to stay in your own lane until level 6 then try to stay alive in your lane as long as possible.Farm as much as possible then recall when the area is safe and you wont be tower dived against.
Another big key in the early lanning phase is harassing with your Q. As you will most more than likely be facing other AP's in the middle the range on your Q is bigger than most so try to keep them back , this helps you farm easier.
When you come back into the lane that's when the fun starts for you !
The runes I picked maybe a little different than most. Reason being is that, for what I lack in defensive items I make up for a little bit in this area.
Magic Pens marks - is the norm for Kassadin.
Greater Seal of Fortitude - for extra HP is KEY for this play style. I can't tell anyone enough how many times I've walked away from a fight or from a gank mainly because having extra health, it works out very well at all levels of play. Getting away with 40 hp and downward really makes these pay off. Not every game with Kassadin are you going to destroy the other team with brute force therefor staying alive is important as well.
Greater Glyph of Force - this is also the norm for Kassadin builds, in order to build late game ability power.
The only real switch in the items is going for the Void Staff before the Lich Bane if the other team is building heavy Magic Resistance against your team mid game.
The main reason for not having any defense items like Banshees Vial is the fact that with Kassadin, late game if hes going to be hit just teleport out with your Ult. If your alone and running into groups of 3+ then your doing something wrong in the first place ( try to stick with someone, ganking from the sides is your best friend ).
Also remember mid-late game, don't be afraid to tower dive for a quick burst kill when Force Pulse is up for you and don't forget your best friend Ignite ( if you choose to pick this ), you can kill someone in a matter of seconds without even being hit.
The key to making this build work is that your going to be doing heavy damage at the price of being extra squishy late game. Mid game on the other hand is where you will shine, If your playing with your in the middle lane, remember Kassadin isn't going to be able to win 2v1 fights vs late game characters. But he can harass by popping in and out of combat while staying safe.