Hey there! I'm your standard Kassadin main, however I thought I would just share my insight on the champion as I have seen a lot of guides for him but I feel they have not been clear on what I feel is important for the champion, so this guide is my attempt at giving you guys a better idea of how you should be thinking when playing Kassadin.

Pros
[*] One of the highest mobility champions in the game
[*] Awesome late game
[*] Passive damage reduction vs magic damage
[*] Single target burst is insane
[*] Insanely fun to play
[*] Mana back from his W
[*] Low cooldown abilities early in the game

Cons
[*] Can be shut down easily
[*] Very vulnerable without his mobility
[*] CANNOT deal with tanks, his only targets are squishies
[*] Riftwalk costs can ramp up quickly
[*] Leveling up his skills does not reduce the cooldown for them, you have to buy CDR yourself if you want lower cooldowns

Flash- Required. End of discussion

Ignite - Assassins love this. Winning lane is part of winning game, especially for champions like Kassadin that snowball so hard and need their late game.

Teleport - In Completely winning matchups take teleport, as you don't need it to win lane and it is much more useful late game for having map presence and assisting other lanes

Exhaust - Vs some AD assassins if you just want to survive. Also helps when you're split pushing and it can be used to turn a fight when doing so, allowing you to grab so cheeky turrets for your troubles.

The only items I think you are required to get to be effective are Rod of ages, Rabadons death cap, Ionian boots and Void staff.
Rod of ages- The Health for survivability and mana for those multiple rift walks and 100 AP
Rabadons death cap - You need as much damage, and this is THE damage item AP champions
Ionian boots - The cooldown on your skills do not go down by leveling up your abilities, and you don't NEED the 15 magic penetration, as getting off more skills makes up for the magic pen
Void staff - You WILL encounter tanks in most games, and you can't just ignore them, so this makes you deal meaningful damage to them.

In terms of optional items
Lich bane - this item is super good as it gives cdr and that sweet sweet sheen proc. Helps you split push and makes your W do so much damage. You can get the sheen proc really easily too, weaving auto attacks after your rift walks.
Athenes - The mana regen after kills and the cdr for your spells. This item is considered core by a lot of kassadin mains. Also a little bit of MR always helps.
Abyssal Scepter - Lovely mr and the magic pen which is perfect as you are in auto attack range for all of your burst.
Zhonyas Hourglass - The active is amazing and required for some match ups. The armour is nice and the 100 AP is great for Kassadin.

As I said earlier, the runes and masteries I posted are to help with your sustain early game. You can be taken advantage of early by smart junglers and laners and you need to make sure you get past that. A lot of people say Kassadin has a weak early game, however I personally disagree. He can cs well under turret with his W and the passive on his W, he can harrass and get a shield from his Q, and he can slow aggressive laners with his E. Sure the base damages are low but if you combo right, you can get trades off without giving the enemy the ability to reply to it. If you can survive or thrive in the early game, and you know your job as a Kassadin, you can win the game.

Once you have 2-3 completed items, you are ready to do what a Kassadin does best, which is team fight. You can re-position yourself very easily and your goal, is the enemy ad carry. A full combo should chunk an ad carry, killing them, or forcing them to run for the fight. Now its a 5v4 where you have a marksman and the enemy does not. If you go in and the enemy team is able to peel you off the ad carry, use your zhonyas if you have it, back off a bit, and go RIGHT back in when your cooldowns are back up. Once the ad carry is dead or running for their base, find another squishy or leave the fight to push a lane. Choice depends on how the fight is going. If its going badly but you KNOW you can make the difference, stay and fight maybe picking up more kills and assists in the process, however if you can see your team still getting slaughtered, go and push a lane, there is no point staying in a losing fight if you cannot make a difference as your better off putting some pressure somewhere on the map. This is important as you are still just trying to get to your late game, which you can't do while having a death timer.

Here you are, after all that time of farming you are finally at your win condition, Kassadin late game. Your job remains the same, however at full build, you have the ability to kill multiple squishies in a very short time window. The moment you focus a tank with an adc with 6 items is focusing you is the moment you have failed. Despite having some armor and hp, you will still get shredded and once you are dead, the backline threat is greatly reduced. Stick to your job. There may be another late game threat that your whole team wants to focus, however you only have one target, once you have killed them you redirect your focus. Feel free to split push too, but when doing so try avoid using your rift walk to clear waves as part of your combo as you may need multiple riftwalks to get out of a 3-4v1 situation and those mana costs add up.

[*] When to pick Kassadin? He's an assassin, which is associated with a high risk, high reward playstyle. However I feel this does not apply to Kassadin. The time to pick him, is any time you see a matchup that you're comfortable with, and when the enemy team lacks much point and click cc or peel. That way you can do your job as best as you can.
[*] Maxing E over Q is a personal choice. Q is the more defensive option and E is the more aggressive option in my opinion. I prefer to be more aggressive in lane as playing an assassin you should always be thinking about when you can go aggressive and E has the slow and the aoe. When you have to be aggressive early game this is what you should always max. HOWEVER, I will agree that in some cases it is VERY RECOMMENDED.
[*] Second item choice is also personal choice. I will always buy the item that gives resistances to the enemy laner as well as AP (unless there is a very fed member on the enemy team that I must account for). This just makes me feel more dominant in the lane, which creates pressure, kill potential and gives the rest of your team more confidence in your ability (which is important for winning games). If your team lacks damage, then take it upon yourself to bring the damage and go Lich bane, Morellonomicon or Rabadons death cap (rabadons less advised as the multiplier is not that effective earlier on)
[*] Riftwalking in lane takes experience to get the hang of, I still get a bit shaky with it. There's always the risk that when you Riftwalk in, the jungler walks out of the bush and ganks you. Riftwalking in lane should be saved for part of your combo (R-E-Q then back off) or clearing waves near the turret. It SHOULD NOT be used to push the wave in the middle or their side of the lane unless you know that if the jungler comes, you will be destroying them too.
[*] Roaming - If you're ahead, I highly recommend this. After all, unless you're 13/2 at the 15 minute mark you won't be carrying this game yourself. You want to look for a lane that is struggling where you can burst down the enemy (so no tanks). This often means you will start your adc murdering days a bit early as top lane has tanks and bruisers. However if you have the choice, going top lane is usually better as you will be planning on killing the enemy adc in fights anyway, so getting your front line ahead is more important.
[*] Warding - You want to keep your yellow trinket until after the laning phase where you change to the blue trinket. During the laning phase when you have time you want to be invading with your jungler and putting wards on the enemy junglers camps. This gives you vision of them so you can prepare you game plan for the next minute and you can even roam into their jungle and pick up a cheeky kill on the enemy jungler while they've been damaged by jungle camps. Snowballing is important on all assassins so you want to pick up any of these "free kills" when you can and will also put the enemy jungler behind while making them ward and play defensively .

I'm in no way a high elo player, I'm only silver, I don't play ranked much as I don't like the stress from it or how people act in ranked games (50% toxic, 50% afk at 15 minutes). Also I played most of my ranked games back when I hit level 30 earlier this season, so I don't really play it due to experience. However I do have a VERY high winrate with Kassadin through normal games I have played on my account with all but a few being games with positive scores (most of these positive scores being games I was fed), which is why I feel like I have the insight to talk about this champion. I feel confident enough to blind pick this champion and I want you to be able to do the same as he is just too much fun.

Hope you enjoyed my first guide! If you have any tips please comment and I'm more than happy to answer questions if you have any. Also please tell me if my guide helped you ^^ (feel free to post stats of games you did well using some of my tips)

Make sure you practice this champion before you take him into ranked. He is in no way an easy champion to just "pick up", I fed super hard the first 3 games I played him, however once you get this champion down and learned, you will have so much fun and gain elo while doing ;) And if you wanna play this champion, make sure you use the Cosmic Reaver skin, its gorgeous :P