Hey guys,
My name is Necrobane012 and I will be making this Malzahar guide because I feel like it has been too long since someone made one for him. Please let me know if this helps ya'll.

On my runes, I take:

Magic Penetration Marks x9
Mana Regen per Level Seals x9
Flat AP Glyphs x9
Flat AP Quints x3

I take this because you of course want magic penetration as much as possible early game. The mana regen helps, especially with your e because you can just start spamming it whenever you want. The flat AP glyphs and quints help you last hit easier early game and help you get kills easier.

For my masteries, I go 21/0/9. I do this simply because the 21 in offense gives me more AP, magic penetration, and increased damage. What's not to love about that? I also get the perk Summoner's Wrath because after you use ignite that's even more AP for you! Then, I put the 9 in the utility tree so I can have more mana, more mana regen, flash cd will be shorter, and my buffs last longer.

With my build, you become this AP carry that has nearly 3k health when you have all items and full stacks on Rod of Ages. With this being said, you still have like 600AP if not more by the time you get all your items as well. That's a lot of power for someone with as much HP as you'll have.
Now down to business. The reason you start off with boots, 2 health pots, and 1 mana pot is simple: the boots make you move fast enough that you should be able to dodge any skill shots that the other mid will probably have and the potions will give you a little sustainability. During the early game while you only have these three items, you want to get as many creeps as you can. Your goal should be to try and get 100 creeps every 10 mins. If you can do that, you will become unstoppable in mid because your damage will soon out do theirs because you will be able to your items sooner. Once you have enough money catalyst, try to get a gank on mid (if you have a jungler). The reason you want this is because if you kill them, that's more money for you. If you don't kill them, more than likely they very low on health so they have to go back and they can't try to get ahead with experience while you are gone getting your items.
After you have your catalyst, your goal is to get as much money as fast as possible so you can get your Rod of Ages as early as possible. You want this because you want to get the full stacks as soon as possible. It takes 10 mins for the Rod to get full stacks so you need that as early as you can get it. Once you get this, then your build becomes situational. Say you have been dominating mid and you have no deaths and you already have 2k gold, go ahead and buy the Needlessly Large Rod for your Deathcap. If your about equal at mid with your opponent, then proceed to buying your Crystal Sceptor starting with the Giant's Belt. If you keep barely dying to your enemy before you can get another skill off, go ahead and build your Hourglass. This way you can pop it while a skill is on cd and use it when you can move again. After you purchase one of these 3 items, the rest is up to you on when and what you buy.

When you play as Malzahar, you want to run ignite and flash for simple reasons.

Ignite: Gives you extra damage when you unleash your entire combo on someone, and if you get the perk, you get extra AP too! It can also give you that early kill whenever the person is barely going to get away but you pop an ignite on them and they run into the fog of war and all of sudden you see on your screen "Necrobane012 has slain Noobcake24".

Flash: you run flash for two reasons. 1st reason is so you can get out of a tight spot. If the enemy jungler comes to gank you, then you can flash out of it and get out of trouble. You can also use it offensively. You can use it to flash in and get your full combo off on someone, and if they are barely getting away with any health, pop ignite and wait and watch the message appear on your screen "Necrobane012 has slain Noobcake24".

I have now shown ya'll how I play Malzahar. This is not a guide saying this is the only way to play him. This is just how I play him. If you don't agree with it that's fine but please don't be a jerk and stupid things just because you don't agree with it. I don't mind constructive critique.