First of all I want to explain why I write this guide:
Malzahar was the first Champion I ever bought, but I didnt find a guide really helping me especially in terms of Items!
I watched some Pro Malzahar players to get an idea how he should be played.
So here are my ideas..

Pros:

- good midlane control
- great ganker
- great for teamfights
- AoE/nuke/silence

Cons:

- focused = dead
- needs some fast levels
- needs a lot of farm
- all about positioning

I decide to go for 9/0/21 for simple reasons:

In the offensive tree you will mostlikely find Archaic Knowledge , Sorcery and Archmage's Savvy to be very helpfull for you as an AP champion. How ever you need one more point in this tree so spend this point in Deadliness , because the other two masteries are even less helpfull.

In the utility tree are even more good masteries for you!
Especially Awareness is just great for solo champions and carries.
I found it more powerfull to get full Good Hands and Perseverence instead of Utility Mastery . Blink of an Eye is really great for Malzahar, because he really needs Flash as much as possible. Quickness is really good as well because of the low movementspeed of Malzahar and the delayed Sorcerer's Shoes. Presence of the Master lowers the cooldowon of Ignite and especially of Flash even more.
Intelligence is just great as well for every AP Champion.

Malefic Visions + Null Zone + Ignite + Nether Gasp + Call of the Void (if needed) = Kill in early and midgame. That is your formula for Malzahar.

Summon Voidling: Great for harrasing your opponent a lot together with Malefic Visions. If you want to Nether Grasp someone early, it is really helpfull to watch out, if your voidling is ready to spawn with your spells.

Call of the Void: Reall good for mid and lategame in teamfights. Try to silence as much opponent champions as possible in teamfights. The most important target is however the opponent AP champion(s). It is really great to finish off low hp champions as well.

Null Zone: Really helpfull in lategame and essential for your "Combo of Death", so skill it just one time as you hit level 4.

Malefic Visions: The best spell in early game for laning. Try to get as many Malefic Visions on your opponent as much and DONT push to much with it in the laning phase.

Nether Grasp: In early and mid game really powerfull to pick someone off together with your "Combo of Death". In teamfights you are able to pick someone just out of the teamfight. But be sure that you are in a save range and cant be interrupted.

Greater Mark of Magic Penetration: Armor penetration is just great to get some nuking power in early and mid game. Especially because your delayed Sorcerer's Shoes

Greater Seal of Scaling Ability Power: Some AP for AP carries like Malzahar is never wrong.

Greater Glyph of Scaling Cooldown Reduction: Helps you out in teamfight, because if you are on cooldown you are as usefull as a Twitch in teamfights.

Greater Quintessence of Magic Penetration: Just some more magic penetration.. FOR THE NUKING POWER!

Early game:

Pick up a Doran's Ring at the start, because it is just the best early game for you out there! Then pick up your Boots and a second Doran's Ring, unless you are able to buy a Catalyst the Protector already. This item should give you a lot of laning ability in early.

Core item

Rabadon's Deathcap: NO DOUBT! The best AP item in the game! Gives you just massive AP and even more, with new AP items. This is also the reason for the delayed Sorcerer's Shoes, which you should pick up right after. Your Catalyst the Protector will be mostlikely go in a Banshee's Veil, unless you got no problems at all against the other AP champion(s).
But be carefull, if there are stuns like Ashe Enchanted Crystal Arrow or something like that. in 95 % of your games you will need Banshee's Veil. In the other 5 % you might go Rod of Ages for more AP.

Late game:

Now its time to get massive more AP. A Void Staff will be very helpfull against the tanks, which already should have a lot of magic resist. Rylai's Crystal Scepter gives you some survive ability and a slow for you AoE`s what is awesome in lategame. If you still struggle against AP with Banshee's Veil you might get a Abyssal Mask.
But my experience is that you will need at least some armor against AD carries so late in the game so my itemchoice is mostly Zhonya's Hourglass, what might save you from death with its active, too.

Ignite: Really good in early game to make the "Combo of Death" a sure kill.

Flash: Essential for Malzahar in my oppinion. You might espace with it threw walls or Flash to your victim to use the "Combo of Death".

First of all: I would go everytime go on a solo lane! Malzahar need this fast levels and his own farm to be really effective for the team.
However the second thing is DONT FARM WITH YOUR Malefic Visions ENTIRE CREEPWAVES!
You will push to much forward! Sure if you need some mana and there is a big wave next to your tower you are allowed to use but not if you are staying there in the middle of the lane! You will be ganked out by opponent junglers, because your pushing power is just sick with that spell. Use Malefic Visions more to harras the opponent down and maybe pick up a kill as you hit level 6 and got your "Combo of Death".

In mid and late game you can push really fast with your Call of the Void and farm entire creepwaves in a matter of a few seconds.
With your Malefic Visions you will be able to restore mana really quickly as well.

You will go in teamfights like this:
- put a Call of the Void, where you hit most of them.
- place your Null Zone at the target of your choice
- now put on the same target your Malefic Visions
- still put your Nether Grasp on the same target which you want out of the fight
- now beginn from the same with Call of the Void

The reason for this is simple: YOU ARE ON COOLDOWN AS USEFULL AS AN INVIS Evelynn STAYING AROUND!. Well maybe your crits of Deadliness will help you.. NOT!

And as i said before, you need to be in save range for you ulti so you dont get interrupted or focussed. Flash might help you out here as well.

Thank for reading and I hope you will nuke some faces in LoL right now ;)
The "Combo of Death" needs some practice, especially to use all your keys in the right order and fast enough before your opponent Flash out himself.

Give me some feedback and your oppinion on this guide
Thank you :)