<<<<<Guide is still a WIP more to come!>>>>>
This is my basic strategy to dominate mid against most champs and with a kill or two become an unstoppable killing machine.
I have hundreds of games with Kassadin, and if I had to choose a main it would definitely be Kassadin.
Since not everyone reads past the introduction...
This is not a guide to be followed to the dot!
If you build this way every single game you will loose. This is meant to be a starting platform and if you read further I will tell you where the most flexible places are.

Greater Mark of Insight - The magic penetration provided from these runes work beautifully with Kassadin and synergizes well with the +15% penetration from masteries and the +20 Magic Penetration from Sorcerer's Shoes. Unless your opponents fear you enough to start building magic resistance (as they should) this should be all the magic pen you need.

Greater Seal of Clarity and Greater Seal of Replenishment Greater Seal of Replenishment - These runes provide good mana regeneration for early game, they're necessary due to the high costs of your spells. Why both flat and scaling Mp5? The flat Mp5 is good for pre-riftwalk harass, and the scaling are better for after you hit 6. You could build either way, I personally like this and have better uses for my IP.

Greater Seal of Focus - Makes all of your spells that much more spammable, why not? (You could probably switch these out for scaling CDR - your preference)

Greater Quintessence of Warding (MR Quints) - Quintessences are the most flexible runes - I prefer the survivability that comes with the magic resist but almost anything else would be fine:
Ability Power - Good for early game harass
CDR - For reasons stated above
Magic Pen - For reasons stated above

Starting Items:
1.) Start out with a Sapphire Crystal and two Health Potions
2.) Your first Item you will want to rush will be a Catalyst the Protector Catalyst the Protector (Survivability, Mana, and the passive is a nice laning boost)

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Early Game:
3.) (Build these items according to your needs)
3.a) Amplifying Tome into Mejai's Soulstealer should be built first if you are dominating mid or have a jungler who can/had successfully ganked.
3.b) Boots of Speed into Sorcerer's Shoes gives you your mobility which should be built first if you are having trouble with someone like Karthus or Ezreal and their skill shots.
3.c) Tear of the Goddess should be built if you are having mana problems or want to get a quick start on building mana for your archangel's.

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Mid/Late Game:
4.) How are you doing?
4.a) Are you getting stacks on Mejai's? Get Rabadon's Deathcap
4.b) Are you spamming your spells but not getting fed? Get Archangel's Staff
4.c) Getting your *** kicked? Get Banshee's Veil

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Late, Late Game:
5.) Assuming the game isn't already over:
5.a) Abyssal Scepter for if they try to counter you with MR.
5.b) Lich Bane will help you get a larger burst and a huge overall dps increase if you are allowed to spam your spells while meleeing.
5.c) MOAR Archangel's Staffs! For when you just can't get enough AP.
5.d) Will of the Ancients if you need to be able to sustain damage over long fights (also more AP).

Weapon Mastery - Kassadin's Passive. Keep this passive in mind when you are mid. It will not allow you to tank, but keep it in mind when fighting a mage. When all of their moves (and yours) are on cooldown, the massive damage you probably took boosted your attack speed many fold.
Null Sphere - Kassadin's Q. A heavy silence, decent range and good damage; this is your harassing spell early game, and in teamfights, this is what you use on a mage.
Nether Blade - Kassadin's W. This move is in need of a rework and is essentially good for giving your Force Pulse stacks.
Force Pulse - Kassadin's E. Massive damage and slow in a large cone on a short cooldown. It's only limiting factor is the need to have 6 stacks ready. (Remember your own spells count!)
Force Pulse can also be used as a passive detection system
- By keeping <6 stacks on your Force Pulse you can detect nearby enemy champions using abilities - even if they are not in sight! This is good for checking Baron/Dragon without having to facecheck.
Riftwalk - Kassadin's Ultimate. Highly spammable teleport with increasing damage on successive casts, but higher mana costs. This (along with cleanse) allows you to be *almost* gank-proof. Use this to jump into range for your Q and E harrass, or stack it in teamfights to deal massive AOE damage.

Cleanse - Good for getting out of ganks, and in teamfights allows you to port onto a target and, despite their efforts, port back to a safe distance.
Ignite - Very helpful for that last chunk of health to earn you a kill as your opponent retreats into their tower early game. Also good for those reliant on lifesteal, spellvamp, or health regen (Swain and Mundo are two that come to mind).

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Some options:
Clairvoyance - Throwing a point from Expanded Mind into Mystical Vision allows this to be substituted in with relative ease. I often use this in place of Ignite, when your team has enough ignites as it is or you have a global ultimate character (Nocturne synergizes beautifully with Clairvoyance as well).
Ghost - Synergizes well with Riftwalk in chases (and escapes) and masteries can easily be changed to accomodate. Not my first pick but viable.
Teleport - This used to one of my spell choices but a few smartly used Riftwalks can land you back at your tower in no time, with almost full mana. No longer my first pick but viable.

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What you should avoid:
Clarity - A decent summoner spell for Kassadin by all means but if you need Clarity this isn't the guide for you.
Flash - You already have one with roughly a 250 second shorter cooldown.

Priorities:
1.) Last hitting minions
- Your main priority mid is to make as much gold as possible. You will have to learn to time your melee attacks which will be difficult due to the presence of an enemy champ