I've seen a few Kassadin builds on this site, and there for the most part good, but I made some changes to some base builds that I feel are better.

Pros:
Great nuke
Insane burst damage
Amazing at escaping
can kill almost any champion late game

Cons:
Squishy
Targeted if you get too close
if stunned in a team fight he's useless
hard to master

Null Sphere
Force Pulse
Null Sphere
Nether Blade
Null Sphere
RiftWalk
Null Sphere
Force Pulse
Null Sphere
Force Pulse
RiftWalk
Force Pulse
Nether Blade
Force Pulse
Nether Blade
RiftWalk
Nether Blade
Nether Blade

most Builds I've seen don't even pick Nether Blade until the end, I feel that this is a very BAD decision. This is a MUST because early game he IS mana hungry, this helps stop that. Your able to stay in the lane longer and able to do more damage by being able to use your Null Sphere more often. Yes you can go and get the golem buff but this help even with that.

I chose these masteries because I just Feel it gives you the best boost for Kassadin, this is also for a lot of other casters.

Marks - Greater Mark of Insight

I picked these because These are by far the best marks I know for Kassadin because of the magic pen

Seals - Greater Seal of Warding

I picked these because it just gives you that extra protection from other mages and spells making you less squishy

Glyphs - Greater Glyph of Focus

I picked these because who doesn't like that extra cooldown reduction

Quintessences - Greater Quintessence of Fortitude

I picked these because it just gives you the extra health you need to stay alive early and later on in the game

WARNING: A lot of text! This is my first build so I'm not sure how to put the item images in, if you can tell me leave a comment please xD.

Anyway:

Start out with the Sapphire Crystal and 2 Health potions. Then once you get about 600 gold port back to your base and pickup a Tear of the Goddess. Some people like the Catalyst but I prefer the tear because early game if you try your spell combo: R -> Q -> E (-> R -> Q) if needed, you will be mana starved, the tear just helps you keep more mana and gain more for later on. Then once you have the tear and you get enough gold for a piece of your Evil tome, or your getting harassed too much go back and buy your boots and a piece. You should be good for a little while and just gank/ harass your lane. Once you get enough go back and finish off your Evil tome. By then your team should be either doing good, having a few towers or your team getting pushed hard. the reason why I went with the tome is because its just safety, if by the time you get your boots know your team is going to win, by all means get mejai's. By this point just get your upgraded boots then your archangels. By this point you should already know you won, or know you lost. Just get your banshie's then your death cap and you should be set. The only time you should have time to get your lichbane is if the game takes a little while longer. If this happens, you can easily take down almost any champ (besides tanks) in just your simple R-> Q -> E

I mentioned this a little bit in the Items section but:

To Harass:

just work your Q if they get too close, if your level 6 then just R -> Q -> E as a simple harass

In Teamfights:

NEVER be the first to go in! unless its 3v1 or better odds you WILL get targeted fast.
make sure you stay behind most of your team, and just R -> Q -> E the squishies, this should give your team a good target or get you a kill. Also good for targeting their carries.

1v1:

If its any great 1v1 champ i.e WW, GET THE HELL OUTTA THERE, slow him with your E if he's close enough and then just R over a wall or to your turret until your team can come back.
BUT if you have a level advantage or health advantage by all means take the kill.

other than that the only champion I would be careful with is Mal, he is one of the few champions that can beat you because of his ultimate and his silence.

Escaping:

This is one of Kassadins strongest areas, escaping. If your all alone and their team starts coming up, or you lose a team fight. You can just E them if there close already and R over a wall to safety.

To farm just try and stay back and last hit with your Q, or you can use your Q to harass and just last hit them normally.

Please try this build out at least a few times before commenting or rating on it, you may get bad teammates or your just not used to it yet. the point is just don't try it once and say it sucks, I've had a lot of successful games with this build and even with we lose I usually come out of it with a positive if not a 2 KD.